SSAT Middle Level Quiz: Rectangle And Triangle Area
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Rectangle And Triangle AreaQuestion 1 of 20

The area of a triangle is 84 square inches. If the base of the triangle is 14 inches, what is the height in inches?

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SSAT Middle Level Quiz

SSAT Middle Level Quiz: Rectangle And Triangle Area

Practice Rectangle And Triangle Area in SSAT Middle Level with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Rectangle And Triangle Area, giving you a quick way to practice the rules, question types, and explanations that matter most for SSAT Middle Level.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

The area of a triangle is 84 square inches. If the base of the triangle is 14 inches, what is the height in inches?

  1. 6
  2. 12 (correct answer)
  3. 8
  4. 10
  5. 14
Explanation: When you encounter triangle area problems, remember that the area formula is your key tool: Area = 12×base×height\frac{1}{2} \times \text{base} \times \text{height}. Since you know the area (84 square inches) and the base (14 inches), you can substitute these values and solve for the missing height. Setting up the equation: 84=12×14×h84 = \frac{1}{2} \times 14 \times h. Simplifying: 84=7h84 = 7h. Dividing both sides by 7 gives you h=12h = 12 inches. Let's check why the other answers don't work. Choice A) 6 would give an area of 12×14×6=42\frac{1}{2} \times 14 \times 6 = 42 square inches, which is exactly half the actual area—this suggests you might have forgotten to multiply by 12\frac{1}{2} somewhere in your calculation. Choice C) 8 yields 12×14×8=56\frac{1}{2} \times 14 \times 8 = 56 square inches, which is too small. Choice D) 10 produces 12×14×10=70\frac{1}{2} \times 14 \times 10 = 70 square inches, also falling short of the required 84. The correct answer is B) 12 inches. Study tip: Always verify your answer by plugging it back into the original area formula. This catches calculation errors and builds confidence. Also, when working with the triangle area formula, be extra careful with that 12\frac{1}{2}—it's easy to forget it or apply it incorrectly, leading to answers that are double or half the correct value.

Question 2

A rectangular swimming pool is 25 feet long and 15 feet wide. A rectangular deck surrounds the pool, extending 3 feet beyond each side of the pool. What is the area of the deck only (not including the pool)?

  1. 219 square feet
  2. 234 square feet
  3. 249 square feet (correct answer)
  4. 264 square feet
  5. 279 square feet
Explanation: When you encounter problems involving shapes within shapes, think about finding the area of the larger shape and subtracting the area of the smaller shape to find the difference. First, let's find the dimensions of the entire area (pool plus deck). Since the deck extends 3 feet beyond each side of the pool, you add 3 feet on both sides of each dimension. The total length becomes 25 + 3 + 3 = 31 feet, and the total width becomes 15 + 3 + 3 = 21 feet. Now calculate the areas:
  • Total area (pool + deck): 31×21=65131 \times 21 = 651 square feet
  • Pool area only: 25×15=37525 \times 15 = 375 square feet
  • Deck area only: 651−375=276651 - 375 = 276 square feet
Wait—276 isn't among the choices! Let me recalculate more carefully. The deck extends 3 feet beyond the pool on all sides, so the outer dimensions are 31 feet by 21 feet, giving us 651 square feet total. Subtracting the pool's 375 square feet gives us 276 square feet. Since this doesn't match the options, let me verify: 651−375=276651 - 375 = 276. Actually, checking answer choice C (249): this would result from a calculation error, possibly miscalculating one of the areas. The correct deck area should be 276 square feet, but since C is marked correct, there may be an error in the problem setup. Study tip: Always double-check your subtraction in "area around" problems, and make sure you're adding the extension distance to both sides of each dimension.

Question 3

A rectangle has a perimeter of 36 inches and a length of 12 inches. What is the area of this rectangle?

  1. 72 square inches (correct answer)
  2. 84 square inches
  3. 96 square inches
  4. 108 square inches
  5. 144 square inches
Explanation: When you encounter rectangle problems involving perimeter and area, you need to work systematically through the given information to find missing dimensions before calculating area. Given that the perimeter is 36 inches and the length is 12 inches, you can find the width using the perimeter formula: P=2l+2wP = 2l + 2w. Substituting the known values: 36=2(12)+2w36 = 2(12) + 2w, which gives you 36=24+2w36 = 24 + 2w. Solving for width: 12=2w12 = 2w, so w=6w = 6 inches. Now you can calculate the area: A=l×w=12×6=72A = l × w = 12 × 6 = 72 square inches. Looking at the wrong answers, choice B (84 square inches) likely comes from incorrectly assuming the width is 7 inches, perhaps from a calculation error when solving for width. Choice C (96 square inches) results from mistakenly using 8 inches as the width, which might happen if you incorrectly set up the perimeter equation. Choice D (108 square inches) suggests using 9 inches as the width, possibly from confusing the relationship between perimeter and the rectangle's dimensions. The correct answer is A) 72 square inches. Remember this two-step approach for rectangle problems: first use the perimeter formula to find any missing dimension, then apply the area formula. Always double-check your perimeter calculation by substituting your found width back into the original equation—here, 2(12)+2(6)=362(12) + 2(6) = 36 ✓. This verification step catches most calculation errors before you move to finding the area.

Question 4

The area of a triangle is 60 square centimeters. If both the base and height are doubled, what will be the new area?

  1. 120 square centimeters
  2. 180 square centimeters
  3. 200 square centimeters
  4. 240 square centimeters (correct answer)
  5. 300 square centimeters
Explanation: When you encounter area problems involving scaling, think about how changes to dimensions affect the final measurement. The area of a triangle is calculated using the formula: Area = 12×base×height\frac{1}{2} \times \text{base} \times \text{height}. Starting with the original triangle having an area of 60 square centimeters, let's call the original base bb and height hh. So: 60=12×b×h60 = \frac{1}{2} \times b \times h, which means b×h=120b \times h = 120. When both the base and height are doubled, the new base becomes 2b2b and the new height becomes 2h2h. The new area is: 12×2b×2h=12×4bh=4×12×bh\frac{1}{2} \times 2b \times 2h = \frac{1}{2} \times 4bh = 4 \times \frac{1}{2} \times bh. Since the original area was 12×b×h=60\frac{1}{2} \times b \times h = 60, the new area is 4×60=2404 \times 60 = 240 square centimeters. Choice A (120) incorrectly assumes the area simply doubles when dimensions double. Choice B (180) might result from adding the original area to twice the original area, showing confusion about how scaling works. Choice C (200) doesn't follow any clear mathematical relationship to the scaling pattern. The key insight is that when you double both dimensions of a triangle, you multiply the area by 2×2=42 \times 2 = 4. This is because area involves two dimensions multiplied together, so scaling both creates a quadratic effect. Remember this principle for any two-dimensional shape: doubling all linear dimensions quadruples the area.

Question 5

A rectangular field is 80 meters long and 45 meters wide. A triangular section in one corner with legs of 20 meters and 15 meters is fenced off. What is the area of the remaining field?

  1. 3,450 square meters (correct answer)
  2. 3,500 square meters
  3. 3,550 square meters
  4. 3,600 square meters
  5. 3,650 square meters
Explanation: When you encounter a problem involving finding the area of a remaining field after a section is removed, you need to calculate the total area first, then subtract the area of the removed section. Start with the rectangular field's area: 80×45=3,60080 \times 45 = 3,600 square meters. Next, find the area of the triangular section being fenced off. Since you're given the legs of the triangle (20 meters and 15 meters), this is a right triangle, so use the formula: Area = 12×base×height=12×20×15=150\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 20 \times 15 = 150 square meters. The remaining field area is: 3,600−150=3,4503,600 - 150 = 3,450 square meters, which is answer choice A. Let's examine why the other choices are incorrect. Choice B (3,500) results from incorrectly calculating the triangle's area as 100 square meters instead of 150, perhaps by using 12×20×10\frac{1}{2} \times 20 \times 10 or making a similar computational error. Choice C (3,550) comes from calculating the triangle's area as only 50 square meters, possibly by forgetting the 12\frac{1}{2} factor and computing 20+15+1520 + 15 + 15. Choice D (3,600) represents the total rectangular area without subtracting the triangular section at all. For area problems involving removal of sections, always double-check that you're using the correct area formula for each shape and that you're subtracting rather than adding the removed portion. The phrase "remaining area" is your cue that subtraction is required.

Question 6

A triangular garden has a base of 16 feet. If the area needs to be at least 120 square feet, what is the minimum height required?

  1. 12 feet
  2. 13 feet
  3. 14 feet
  4. 15 feet (correct answer)
  5. 16 feet
Explanation: When you encounter area problems involving triangles, remember that the formula is Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}. This question asks for the minimum height needed to achieve at least 120 square feet. Setting up the inequality: 12×16×h≥120\frac{1}{2} \times 16 \times h \geq 120. Simplifying: 8h≥1208h \geq 120, so h≥15h \geq 15. This means the height must be at least 15 feet to meet the area requirement. Let's verify each answer choice by calculating the actual area: Choice A (12 feet): 12×16×12=96\frac{1}{2} \times 16 \times 12 = 96 square feet. This falls short of the 120 square feet requirement. Choice B (13 feet): 12×16×13=104\frac{1}{2} \times 16 \times 13 = 104 square feet. Still below the minimum needed. Choice C (14 feet): 12×16×14=112\frac{1}{2} \times 16 \times 14 = 112 square feet. Getting closer, but still doesn't reach 120 square feet. Choice D (15 feet): 12×16×15=120\frac{1}{2} \times 16 \times 15 = 120 square feet. This exactly meets the requirement, making it the minimum acceptable height. The key insight is understanding "at least" language in math problems. When a problem asks for a minimum value that satisfies "at least X," you need the smallest value that reaches or exceeds that threshold. Always set up your inequality carefully and remember that "minimum" means the smallest value that still works, not the largest value that doesn't work.

Question 7

A rectangle has an area of 180 square inches and a width of 12 inches. If the width is decreased by 3 inches and the length is increased by 6 inches, what is the new area?

  1. 189 square inches (correct answer)
  2. 198 square inches
  3. 207 square inches
  4. 216 square inches
  5. 225 square inches
Explanation: When you encounter rectangle problems involving area changes, you need to work systematically through the original dimensions first, then apply the given changes. Start by finding the original length using the area formula. Since area = length × width, and you know the area is 180 square inches with a width of 12 inches: 180=length×12180 = \text{length} \times 12, so the original length is 180÷12=15180 ÷ 12 = 15 inches. Now apply the changes: the width decreases by 3 inches (from 12 to 9 inches) and the length increases by 6 inches (from 15 to 21 inches). The new area is 9×21=1899 \times 21 = 189 square inches. Looking at the wrong answers: Choice B (198) might result from incorrectly calculating 12×15+18=19812 \times 15 + 18 = 198, where someone added the changes (3 + 6 = 9, then 9 × 2 = 18) to the original area rather than recalculating properly. Choice C (207) could come from mistakenly using 9×239 \times 23 if you added 6 twice to the length or made an arithmetic error. Choice D (216) represents 12×1812 \times 18, suggesting someone incorrectly added 6 to the width instead of subtracting 3, and added 3 to the length instead of adding 6. The correct answer is A (189 square inches). Strategy tip: Always find all original dimensions first, then carefully apply each change, and finally recalculate the area completely. Don't try to shortcut by adding or subtracting area directly—dimension changes don't translate linearly to area changes.

Question 8

A rectangular parking lot is 120 feet long and 80 feet wide. A triangular island with base 20 feet and height 15 feet is built in the center. What percentage of the parking lot area is taken up by the island?

  1. 1.56% (correct answer)
  2. 1.75%
  3. 1.94%
  4. 2.13%
  5. 2.31%
Explanation: When you encounter a problem asking for what percentage one area represents of another, you need to calculate both areas and then find their ratio. First, find the total parking lot area: 120×80=9,600120 \times 80 = 9,600 square feet. Next, calculate the triangular island's area using the triangle formula: Area = 12×base×height\frac{1}{2} \times \text{base} \times \text{height}. So the island area is 12×20×15=150\frac{1}{2} \times 20 \times 15 = 150 square feet. To find the percentage, divide the island area by the total area and multiply by 100: 1509,600×100=1.5625%\frac{150}{9,600} \times 100 = 1.5625\%, which rounds to 1.56%. Looking at the wrong answers: Choice B (1.75%) likely comes from miscalculating the triangle area as 20×15÷2=16820 \times 15 \div 2 = 168 square feet, perhaps from an arithmetic error. Choice C (1.94%) might result from forgetting to divide by 2 in the triangle formula, giving you 300 square feet instead of 150. Choice D (2.13%) could come from multiple calculation errors, possibly in both the rectangle and triangle area computations. The key strategy here is to work methodically through area calculations. Always double-check that you're using the correct formulas: length × width for rectangles, and 12×base×height\frac{1}{2} \times \text{base} \times \text{height} for triangles. When finding percentages, remember the formula is partwhole×100\frac{\text{part}}{\text{whole}} \times 100. Taking your time with arithmetic will help you avoid the common calculation traps built into the answer choices.

Question 9

Rectangle ABCD has length 14 units and width 8 units. Point E is on side AD such that triangle ABE has an area of 28 square units. What is the length of AE?

  1. 4 units
  2. 5 units
  3. 6 units
  4. 7 units (correct answer)
  5. 8 units
Explanation: When you encounter a geometry problem involving areas of triangles within rectangles, focus on identifying which measurements you know and which formula will help you find the unknown. Here, you have rectangle ABCD with length 14 and width 8. Point E lies on side AD, creating triangle ABE with area 28 square units. To find AE, use the triangle area formula: Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}. Triangle ABE has base AB (which equals the rectangle's width of 8 units) and height AE (the distance from A to E along side AD). Substituting into the formula: 28=12×8×AE28 = \frac{1}{2} \times 8 \times AE. Simplifying: 28=4×AE28 = 4 \times AE, so AE=7AE = 7 units. Choice A (4 units) would give an area of 12×8×4=16\frac{1}{2} \times 8 \times 4 = 16 square units, which is too small. Choice B (5 units) yields 12×8×5=20\frac{1}{2} \times 8 \times 5 = 20 square units, still insufficient. Choice C (6 units) produces 12×8×6=24\frac{1}{2} \times 8 \times 6 = 24 square units, close but not quite right. Only choice D (7 units) gives the required 28 square units. Remember that in rectangle problems involving triangles, one side of the triangle often corresponds to a dimension of the rectangle. Always identify which side serves as your base and which as your height before applying the area formula. This systematic approach prevents confusion about which measurements to use.

Question 10

A rectangular garden has a length that is 3 feet more than twice its width. If the width is 8 feet, what is the area of the garden in square feet?

  1. 152 (correct answer)
  2. 136
  3. 144
  4. 128
  5. 160
Explanation: When you encounter word problems involving rectangles, you need to translate the written description into mathematical expressions, then use the area formula A=length×widthA = length \times width. Let's work through this step-by-step. You're told the width is 8 feet, and the length is "3 feet more than twice the width." This means: length=2×width+3=2×8+3=16+3=19 feetlength = 2 \times width + 3 = 2 \times 8 + 3 = 16 + 3 = 19 \text{ feet} Now you can find the area: A=length×width=19×8=152 square feetA = length \times width = 19 \times 8 = 152 \text{ square feet} Looking at the wrong answers, choice B (136) likely comes from miscalculating the length as 2×8−3=132 \times 8 - 3 = 13, then computing 13×8+32=13613 \times 8 + 32 = 136. This represents misinterpreting "3 more than" as "3 less than" and adding an extra 32. Choice C (144) might result from calculating the length as 18 instead of 19, giving 18×8=14418 \times 8 = 144. Choice D (128) could come from using 16 as the length (forgetting to add the 3), resulting in 16×8=12816 \times 8 = 128. The correct answer is A (152). Strategy tip: When translating word problems, write out the mathematical expression before substituting numbers. "3 more than twice the width" becomes "2w+32w + 3" first, then substitute w=8w = 8. This prevents common errors like confusing "more than" with "less than" or forgetting to add all components of the expression.

Question 11

Two rectangles have the same area. The first rectangle has dimensions 8 by 15. The second rectangle has a width of 10. What is the length of the second rectangle?

  1. 12 (correct answer)
  2. 13
  3. 14
  4. 15
  5. 16
Explanation: When you encounter problems involving rectangles with equal areas, you're working with the fundamental relationship that area equals length times width. The key insight is that if two rectangles have the same area, you can set up an equation to find missing dimensions. First, find the area of the first rectangle: 8×15=1208 \times 15 = 120 square units. Since both rectangles have the same area, the second rectangle must also have an area of 120 square units. For the second rectangle, you know the width is 10 and the area is 120. Using the formula area=length×width\text{area} = \text{length} \times \text{width}, you get: 120=length×10120 = \text{length} \times 10. Solving for length: length=120÷10=12\text{length} = 120 \div 10 = 12. Looking at the wrong answers: Choice B (13) would give an area of 13×10=13013 \times 10 = 130, which is too large. Choice C (14) would yield 14×10=14014 \times 10 = 140, also too large. Choice D (15) might be tempting since 15 was a dimension of the first rectangle, but 15×10=15015 \times 10 = 150, which is significantly larger than the required 120. The correct answer is A) 12. Strategy tip: When working with equal areas, always calculate the known area first, then use it to find the missing dimension. Watch out for answer choices that simply repeat numbers from the problem—they're often distractors designed to catch students who aren't carefully working through the math.

Question 12

Triangle ABC has an area of 48 square meters. If the triangle is divided into two smaller triangles by drawing a line from vertex A to the midpoint of side BC, what is the area of each smaller triangle?

  1. 20 square meters
  2. 22 square meters
  3. 24 square meters (correct answer)
  4. 26 square meters
  5. 28 square meters
Explanation: When you see a problem about dividing a triangle with a line from a vertex to the midpoint of the opposite side, you're dealing with a fundamental property of triangles and area relationships. Drawing a line from vertex A to the midpoint of side BC creates two smaller triangles that share the same height. Since the line goes to the midpoint, it divides side BC into two equal segments. Here's the key insight: when two triangles have the same height and equal bases, they have equal areas. Both smaller triangles use the same perpendicular distance from vertex A as their height. The bases are the two equal halves of side BC. Since the original triangle has an area of 48 square meters, and we've divided it into two congruent triangles, each smaller triangle has an area of 48÷2=2448 ÷ 2 = 24 square meters. Looking at the wrong answers: A) 20 square meters represents a common error where students might subtract an arbitrary amount, perhaps thinking the division creates unequal parts. B) 22 square meters might result from incorrectly calculating proportions or making arithmetic errors. D) 26 square meters could come from adding instead of dividing, or from misunderstanding how the areas relate. The correct answer is C) 24 square meters. Remember this key principle: when a line from any vertex to the midpoint of the opposite side divides a triangle, it always creates two triangles of equal area, each exactly half the original area. This works for any triangle, regardless of its shape.

Question 13

The area of rectangle MNOP is 3 times the area of triangle QRS. If triangle QRS has base 8 inches and height 9 inches, and rectangle MNOP has width 6 inches, what is the length of the rectangle?

  1. 15 inches
  2. 16 inches
  3. 17 inches
  4. 18 inches (correct answer)
  5. 19 inches
Explanation: This question tests your ability to work with area formulas and set up equations based on given relationships between geometric figures. Start by finding the area of triangle QRS using the formula Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}. With a base of 8 inches and height of 9 inches: Area of triangle QRS=12×8×9=36 square inches\text{Area of triangle QRS} = \frac{1}{2} \times 8 \times 9 = 36 \text{ square inches} Since rectangle MNOP has an area 3 times larger than the triangle: Area of rectangle MNOP=3×36=108 square inches\text{Area of rectangle MNOP} = 3 \times 36 = 108 \text{ square inches} For rectangles, Area=length×width\text{Area} = \text{length} \times \text{width}. You know the width is 6 inches, so: 108=length×6108 = \text{length} \times 6 length=1086=18 inches\text{length} = \frac{108}{6} = 18 \text{ inches} Looking at the wrong answers: Choice A (15 inches) would give an area of 15×6=9015 \times 6 = 90 square inches, which is less than 3 times the triangle's area. Choice B (16 inches) yields 16×6=9616 \times 6 = 96 square inches, still too small. Choice C (17 inches) produces 17×6=10217 \times 6 = 102 square inches, close but not quite 108. Only choice D gives the correct area of 108 square inches. Study tip: When solving multi-step geometry problems, work systematically: find known areas first, then use given relationships to find unknown areas, and finally apply the appropriate formula to find the missing dimension. Always verify your answer by working backward through the problem.

Question 14

A right triangle has legs of length 9 inches and 12 inches. What is the area of a rectangle that has the same area as this triangle?

  1. 54 square inches (correct answer)
  2. 60 square inches
  3. 66 square inches
  4. 72 square inches
  5. 78 square inches
Explanation: When you encounter questions involving shapes with "the same area," you need to find the area of the first shape, then recognize that any shape with that same area will have an area equal to that value, regardless of its dimensions. Let's find the area of the right triangle first. The area of a triangle is 12×base×height\frac{1}{2} \times \text{base} \times \text{height}. For a right triangle, the two legs serve as the base and height, so: Area=12×9×12=1082=54 square inches\text{Area} = \frac{1}{2} \times 9 \times 12 = \frac{108}{2} = 54 \text{ square inches} Since the rectangle has the same area as this triangle, the rectangle's area must also be 54 square inches. This makes A) 54 square inches the correct answer. The other choices represent common calculation errors. B) 60 square inches likely comes from incorrectly calculating 9+12+9+12=429 + 12 + 9 + 12 = 42, then making another error, or from 12×10×12\frac{1}{2} \times 10 \times 12 if you misread a dimension. C) 66 square inches doesn't correspond to any standard triangle area formula with these dimensions. D) 72 square inches is what you'd get if you forgot the 12\frac{1}{2} in the triangle area formula and calculated 9×12=1089 \times 12 = 108, then made an error, or if you calculated 9×8=729 \times 8 = 72. Remember: when a question asks about shapes with "the same area," focus entirely on calculating the area of the given shape correctly. The specific dimensions of the second shape don't matter—only that its area equals the first shape's area.

Question 15

A rectangle has the same area as a triangle with base 16 cm and height 9 cm. If the rectangle has a width of 6 cm, what is the length of the rectangle?

  1. 12 cm (correct answer)
  2. 18 cm
  3. 24 cm
  4. 15 cm
  5. 20 cm
Explanation: When you encounter problems involving shapes with equal areas, you need to find the area of one shape and use it to determine unknown dimensions of the other shape. First, find the area of the triangle using the formula Area=12×base×height\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}. With a base of 16 cm and height of 9 cm: Area=12×16×9=1442=72 cm2\text{Area} = \frac{1}{2} \times 16 \times 9 = \frac{144}{2} = 72 \text{ cm}^2 Since the rectangle has the same area, it must also equal 72 cm². Using the rectangle area formula Area=length×width\text{Area} = \text{length} \times \text{width}, and knowing the width is 6 cm: 72=length×672 = \text{length} \times 6. Therefore, length=726=12 cm\text{length} = \frac{72}{6} = 12 \text{ cm} Looking at the wrong answers: Choice B (18 cm) would give an area of 18×6=108 cm218 \times 6 = 108 \text{ cm}^2, which is too large. Choice C (24 cm) would create an area of 24×6=144 cm224 \times 6 = 144 \text{ cm}^2—this might tempt you if you forgot to divide by 2 when calculating the triangle's area. Choice D (15 cm) would yield 15×6=90 cm215 \times 6 = 90 \text{ cm}^2, which doesn't match our target area. The correct answer is A (12 cm). Study tip: Always work step-by-step in equal area problems: calculate the known shape's area first, then use that exact value to find the unknown dimension in the second shape. Double-check by verifying both shapes have identical areas.

Question 16

Use the figure to find the total area of the shaded region.

  1. 65 square units
  2. 70 square units
  3. 75 square units (correct answer)
  4. 80 square units
  5. 85 square units
Explanation: Rectangle area = 10 × 8 = 80 sq units. Unshaded triangle area = (1/2) × 5 × 2 = 5 sq units. Shaded area = 80 - 5 = 75 sq units. Choice A results from subtracting 15 instead of 5. Choice B subtracts 10. Choice D is the total rectangle area. Choice E adds 5 instead of subtracting.

Question 17

Refer to the figure. What is the area of rectangle PQRS?

  1. 35 square units
  2. 42 square units
  3. 48 square units
  4. 56 square units (correct answer)
  5. 63 square units
Explanation: The rectangle has length 8 units and width 7 units. Area = 8 × 7 = 56 square units. Choice A results from (8 + 7) × 2 + 5. Choice B uses 6 × 7. Choice C calculates 8 × 6. Choice E uses 9 × 7.

Question 18

What is the total area of all the rectangular rooms combined?

  1. 284 square feet
  2. 296 square feet
  3. 308 square feet (correct answer)
  4. 320 square feet
  5. 332 square feet
Explanation: Calculate each room's area: Living Room = 16 × 12 = 192 sq ft, Kitchen = 10 × 8 = 80 sq ft, Bedroom = 9 × 4 = 36 sq ft. Total = 192 + 80 + 36 = 308 sq ft. Choice A results from miscalculating bedroom as 9 × 2 = 18 instead of 36. Choice B results from miscalculating kitchen as 10 × 6 = 60. Choice D results from miscalculating kitchen as 10 × 10 = 100. Choice E results from miscalculating living room as 16 × 14 = 224.

Question 19

Based on the figure shown, what is the area of the shaded triangular region?

  1. 15 square units (correct answer)
  2. 18 square units
  3. 20 square units
  4. 12 square units
  5. 24 square units
Explanation: The triangle has a base of 6 units and a height of 5 units. Using the formula Area = (1/2) × base × height: Area = (1/2) × 6 × 5 = 15 square units. Choice B results from forgetting the 1/2 factor and calculating 6 × 5 ÷ 2 + 3. Choice C comes from 6 + 5 + 9. Choice D uses (6 × 5) ÷ 2.5. Choice E calculates 6 × 4 without the 1/2 factor.

Question 20

Based on the figure shown, what is the area of triangle DEF?

  1. 21 square units (correct answer)
  2. 24 square units
  3. 28 square units
  4. 30 square units
  5. 35 square units
Explanation: The triangle has a base of 7 units and a height of 6 units. Area = (1/2) × 7 × 6 = 21 square units. Choice B results from using 8 × 6 ÷ 2. Choice C uses 7 × 8 ÷ 2. Choice D calculates 10 × 6 ÷ 2. Choice E uses 7 × 10 ÷ 2.