Elementary School Math Quiz: Solve Perimeter And Area Problems
20 questions · exam conditions
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Solve Perimeter And Area ProblemsQuestion 1 of 20

Jayden wants to put a fence around his rectangular yard. The yard is 1515 feet long and 1212 feet wide. Fencing costs $2\$2 per foot. How much will the fencing cost in total?

$27\$27
$54\$54
$108\$108
$360\$360
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Elementary School Math Quiz

Elementary School Math Quiz: Solve Perimeter And Area Problems

Practice Solve Perimeter And Area Problems in Elementary School Math 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 Solve Perimeter And Area Problems, giving you a quick way to practice the rules, question types, and explanations that matter most for Elementary School Math.

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

Jayden wants to put a fence around his rectangular yard. The yard is 1515 feet long and 1212 feet wide. Fencing costs $2\$2 per foot. How much will the fencing cost in total?

  1. $27\$27
  2. $54\$54
  3. $108\$108 (correct answer)
  4. $360\$360
Explanation: When a question asks about putting a fence around a shape, it's testing perimeter — the total distance around the outside. Perimeter is different from area (which measures the space inside), so watch for that keyword "around." For a rectangle, perimeter means adding up all four sides. Since a rectangle has two lengths and two widths, you can calculate it as: P=2×length+2×widthP = 2 \times \text{length} + 2 \times \text{width}
P=2×15+2×12=30+24=54 feetP = 2 \times 15 + 2 \times 12 = 30 + 24 = 54 \text{ feet} Jayden needs 5454 feet of fencing. Since each foot costs $2\$2, multiply: 54×2=$10854 \times 2 = \$108 That matches choice C. Choice A ($27\$27) comes from only adding one length and one width (15+12=2715 + 12 = 27) — that's just half the perimeter. Choice B ($54\$54) is the perimeter in feet, but forgets to multiply by the $2\$2 per foot cost. Choice D ($360\$360) uses area instead of perimeter (15×12=18015 \times 12 = 180, then ×2=360\times 2 = 360) — a common trap when you confuse "around" with "inside." Study tip: Circle the key word in word problems. "Around," "border," "fence," and "frame" all signal perimeter (add all sides). "Cover," "inside," "carpet," and "paint" signal area (multiply length × width). Getting this first step right is half the battle!

Question 2

Maya has a rectangle that is 10 yards long and 2 yards wide. What is its perimeter?

  1. 12 yards
  2. 20 yards
  3. 24 yards (correct answer)
  4. 22 yards
Explanation: The perimeter is the sum of all four sides: 10 plus 2 plus 10 plus 2 yards, which is 24 yards, matching choice C. Choice A only adds the length and width once instead of going around all four sides. Choice B comes from multiplying the length and width instead of adding all the sides. Choice D leaves out one of the sides from the total.

Question 3

Look at the grid showing two rectangles. Rectangle P and Rectangle Q have the same area. What is the difference in their perimeters?

  1. 22 units difference in perimeter
  2. 44 units difference in perimeter (correct answer)
  3. 66 units difference in perimeter
  4. 88 units difference in perimeter
Explanation: Rectangle P: 2×6=122 \times 6 = 12 square units, perimeter =2(2)+2(6)=16= 2(2) + 2(6) = 16 units. Rectangle Q: 3×4=123 \times 4 = 12 square units, perimeter =2(3)+2(4)=14= 2(3) + 2(4) = 14 units. Difference =16−14=4= 16 - 14 = 4 units. Choice A is half the correct difference. Choice C results from subtracting lengths (6−3=36 - 3 = 3) plus widths (4−2=24 - 2 = 2). Choice D results from doubling the correct answer.

Question 4

A rectangle has area 24 square feet, and its length is 6 feet. What is its width?

  1. 30 feet
  2. 4 feet (correct answer)
  3. 18 feet
  4. 12 feet
Explanation: Area equals length times width, so 24 divided by 6 gives a width of 4 feet. Choice A comes from adding instead of dividing. Choice C comes from subtracting the length from the area instead of dividing. Choice D comes from dividing incorrectly and mismatching units.

Question 5

A rectangle has a perimeter of 24 meters. One side is 7 meters. What is the combined length of the other two sides?

  1. 10 meters (correct answer)
  2. 3 meters
  3. 7 meters
  4. 5 meters
Explanation: Since opposite sides of a rectangle are equal, the two sides of length 7 meters total 14 meters, leaving 24 minus 14, which is 10 meters, for the other two sides combined. Choice B (3 meters) comes from a subtraction error. Choice C (7 meters) repeats the given side length instead of finding the remaining total. Choice D (5 meters) is the length of just one of the two remaining sides, not their combined length.

Question 6

Sofia is buying carpet for a rectangular room that is 9 feet long and 4 feet wide. What is the area of the room?

  1. 36 square feet (correct answer)
  2. 13 square feet
  3. 26 square feet
  4. 18 square feet
Explanation: The area of the room is 9 times 4, which is 36 square feet. Choice B (13 square feet) comes from adding 9 and 4 instead of multiplying. Choice C (26 square feet) uses the perimeter formula instead of the area formula. Choice D (18 square feet) comes from doubling only one side instead of multiplying both.

Question 7

Refer to the figure. What is the perimeter of the shape?

  1. 2121 cm
  2. 2626 cm
  3. 2828 cm
  4. 3030 cm (correct answer)
Explanation: Adding all six sides going around the figure: 7+5+3+3+4+8=307 + 5 + 3 + 3 + 4 + 8 = 30 cm. Choice A adds only some of the sides. Choice B misses one side. Choice C double-counts or misreads a segment.

Question 8

Refer to the table showing four rectangles. Which two rectangles have the SAME area but DIFFERENT perimeters?

  1. Rectangle 1 and Rectangle 2
  2. Rectangle 1 and Rectangle 3 (correct answer)
  3. Rectangle 2 and Rectangle 4
  4. Rectangle 3 and Rectangle 4
Explanation: Areas: R1: 2×12=242 \times 12 = 24; R2: 3×6=183 \times 6 = 18; R3: 4×6=244 \times 6 = 24; R4: 5×5=255 \times 5 = 25. Perimeters: R1: 2828; R2: 1818; R3: 2020; R4: 2020. Rectangles 1 and 3 both have area 2424 but perimeters 2828 and 2020 (different). Choice A: different areas. Choice C: different areas. Choice D: same perimeter but different areas — this is the opposite of what is asked.

Question 9

Two rectangles both have a perimeter of 2020 cm. Rectangle X measures 22 cm by 88 cm. Rectangle Y measures 55 cm by 55 cm. How much larger is the area of Rectangle Y than Rectangle X?

  1. 00 square cm (they are equal)
  2. 33 square cm
  3. 99 square cm (correct answer)
  4. 2525 square cm
Explanation: This question tests an important idea in geometry: two shapes can have the same perimeter but different areas. Perimeter measures the distance around a shape, while area measures the space inside it. For rectangles, area = length × width. Start by finding each area. Rectangle X is 2×8=162 \times 8 = 16 square cm. Rectangle Y is 5×5=255 \times 5 = 25 square cm. To find how much larger Y is, subtract: 25−16=925 - 16 = 9 square cm. That matches choice C. Choice A is a trap for students who assume that equal perimeters mean equal areas — but as this problem shows, a square-like shape holds more area than a long, thin rectangle with the same perimeter. Choice B (33) likely comes from subtracting the side lengths (8−5=38 - 5 = 3) instead of the areas — that's comparing dimensions, not space inside. Choice D (2525) is just the area of Rectangle Y by itself; it forgets to subtract Rectangle X's area to find the difference. A helpful pattern to remember: among rectangles with the same perimeter, the closer the shape is to a square, the larger its area. A 5×55 \times 5 square beats a skinny 2×82 \times 8 rectangle every time. When a word problem asks "how much larger," always finish by subtracting — don't stop after calculating just one value.

Question 10

A hexagon has six sides. Five of the sides measure 44 cm, 66 cm, 33 cm, 55 cm, and 77 cm. If the perimeter is 2828 cm, what is the length of the sixth side?

  1. 22 cm
  2. 33 cm (correct answer)
  3. 44 cm
  4. 55 cm
Explanation: When a shape's perimeter is given, remember that it's just the total distance around the shape — the sum of all its side lengths. If you know the perimeter and all but one side, you can find the missing side by subtracting the known sides from the total. Start by adding the five known sides:
4+6+3+5+7=25 cm4 + 6 + 3 + 5 + 7 = 25 \text{ cm} Since the full perimeter is 2828 cm, the sixth side must make up the difference:
28−25=3 cm28 - 25 = 3 \text{ cm} That matches choice B. Choice A (22 cm) is what you'd get if you added the known sides incorrectly and got 2626 instead of 2525 — a common slip when adding several numbers in a row. Choice C (44 cm) is a trap because 44 cm is already listed as one of the given sides; the question isn't asking you to repeat a value. Choice D (55 cm) is another number pulled straight from the given sides, which tempts students who guess instead of calculating. A helpful strategy: whenever a perimeter problem gives you all but one side, write it as a subtraction sentence — Perimeter − (sum of known sides) = missing side. Double-check your addition by grouping numbers that make friendly tens (like 3+7=103 + 7 = 10 and 4+6=104 + 6 = 10, then add 55) to avoid arithmetic mistakes.

Question 11

Carlos is fencing a square playground. He has 48 feet of fencing, and he uses all of it to build the square fence. Later, he wants to add a path across the middle of the playground, parallel to one side. How much additional fencing does he need for this path?

  1. 6 feet of additional fencing
  2. 12 feet of additional fencing (correct answer)
  3. 24 feet of additional fencing
  4. 48 feet of additional fencing
Explanation: Since the playground is a square made from 48 feet of fencing, each side is 48 divided by 4, or 12 feet. A path across the middle, parallel to one side, is the same length as one side, so Carlos needs 12 feet of additional fencing, matching choice B. Choice A is too short to reach across the playground. Choices C and D use the wrong amount of fencing, mixing up parts of the original square with the new path.

Question 12

Garden B is a rectangle that is 5 feet by 5 feet. What is its area?

  1. 9 square feet
  2. 20 square feet
  3. 25 square feet (correct answer)
  4. 10 square feet
Explanation: Area equals length times width, so 5 times 5 equals 25 square feet. Choice A is the area of a different garden shape, not this one. Choice B is the perimeter of the garden, not its area. Choice D comes from adding the side lengths instead of multiplying them.

Question 13

A rectangle has a perimeter of 26 yards, and one side is 8 yards long. What is the length of the other side?

  1. 5 yards (correct answer)
  2. 18 yards
  3. 9 yards
  4. 13 yards
Explanation: The perimeter equals twice the sum of both side lengths, so 2 x 8 plus 2 times the other side equals 26, which gives the other side as (26 minus 16) divided by 2, or 5 yards, making Choice A correct. Choice B (18 yards) comes from subtracting 8 from 26 without accounting for both pairs of sides. Choice C (9 yards) does not match any consistent method for solving this problem. Choice D (13 yards) divides the perimeter by 2 but forgets to subtract the known side first.

Question 14

Sofia is carpeting a rectangular room that is 9 feet by 6 feet. What is the area?

  1. 54 feet
  2. 15 square feet
  3. 30 square feet
  4. 54 square feet (correct answer)
Explanation: The area of the room is 9 times 6, which is 54 square feet. Choice A (54 feet) has the correct number but is missing the square units for area. Choice B (15 square feet) comes from adding 9 and 6 instead of multiplying. Choice C (30 square feet) uses the perimeter formula instead of the area formula.

Question 15

Maya is tiling a rectangular patio that is 7 feet by 6 feet. How many square feet of tile does she need?

  1. 42 square feet (correct answer)
  2. 13 square feet
  3. 84 square feet
  4. 26 square feet
Explanation: 42 square feet is correct because area equals length times width, and 7 times 6 equals 42. 13 square feet is incorrect because it adds the side lengths instead of multiplying them. 84 square feet is incorrect because it doubles the correct area. 26 square feet is incorrect because it finds the perimeter instead of the area.

Question 16

Use the table to answer the question. Three students each built rectangular gardens with different dimensions but the same total amount of fencing. Which student's garden has the largest area?

  1. Anna's garden has the largest area
  2. Ben's garden has the largest area (correct answer)
  3. Carla's garden has the largest area
  4. All gardens have the same area
Explanation: First verify they used the same fencing: Anna: 2(3)+2(9)=242(3) + 2(9) = 24, Ben: 2(4)+2(8)=242(4) + 2(8) = 24, Carla: 2(2)+2(10)=242(2) + 2(10) = 24. All have perimeter 2424. Areas: Anna: 3×9=273 \times 9 = 27, Ben: 4×8=324 \times 8 = 32, Carla: 2×10=202 \times 10 = 20. Ben's garden has the largest area. Choice A and C select gardens with smaller areas. Choice D incorrectly assumes same perimeter means same area.

Question 17

Look at the shape. What is the perimeter of this polygon?

  1. 2222 centimeters
  2. 2424 centimeters
  3. 2626 centimeters (correct answer)
  4. 2828 centimeters
Explanation: Adding all the labeled sides: 4+3+2+5+6+6=264 + 3 + 2 + 5 + 6 + 6 = 26 centimeters. Choice A results from missing one of the 44-cm sides. Choice B results from miscounting and adding 4+3+2+5+5+54 + 3 + 2 + 5 + 5 + 5. Choice D results from adding an extra 22-cm segment.

Question 18

Refer to the figure. What is the perimeter of the triangle?

  1. 1818 in
  2. 2121 in (correct answer)
  3. 2424 in
  4. 4040 in
Explanation: Add the three sides: 5+7+9=215 + 7 + 9 = 21 inches. Choice A leaves out one side. Choice C adds an extra 33. Choice D confuses perimeter with something like area calculations.

Question 19

Tommy is building a pen for his rabbit. He starts with a rectangular pen that is 44 feet by 66 feet. Then he decides to make it longer by extending the length to 88 feet, keeping the width the same. How much additional fencing does he need for the new sections only?

  1. 44 feet of additional fencing
  2. 1616 feet of additional fencing
  3. 1212 feet of additional fencing
  4. 88 feet of additional fencing (correct answer)
Explanation: When you see a problem about extending or changing the size of a shape, focus carefully on what's being asked. This question wants to know how much additional fencing Tommy needs - not the total perimeter of the new pen. Let's visualize what's happening. Tommy's original pen is 4 feet by 6 feet. When he extends the length from 6 feet to 8 feet, he's adding 2 feet to the length while keeping the width at 4 feet. Picture this: he's essentially adding a rectangular section that is 2 feet by 4 feet to one end of his pen. To fence in this new section, Tommy needs fencing for three sides of this added rectangle (the fourth side is already connected to his existing pen). So he needs: one piece that's 2 feet long, one piece that's 4 feet long, and another piece that's 2 feet long. That's 2+4+2=82 + 4 + 2 = 8 feet of additional fencing. Choice A (4 feet) only accounts for the width of the addition. Choice B (16 feet) calculates the difference between the full perimeters of the old and new pens, but includes fencing Tommy already has. Choice C (12 feet) might come from incorrectly adding all four sides of the 2×4 addition (2+4+2+4=122 + 4 + 2 + 4 = 12), forgetting that one side connects to existing fencing. Remember: when a shape is extended, you only need new fencing for the exposed edges of the addition, not for the side that connects to what's already there.

Question 20

Maya is building two different rectangular pens for her rabbits. Both pens will have an area of 2424 square feet. Pen A is 44 feet by 66 feet. Pen B is 33 feet by 88 feet. Which statement is true?

  1. Pen A and Pen B have the same perimeter.
  2. Pen A has a smaller perimeter than Pen B. (correct answer)
  3. Pen A has a larger perimeter than Pen B.
  4. You cannot compare the perimeters without more information.
Explanation: When two rectangles have the same area, they don't automatically have the same perimeter. Area measures the space inside a shape, while perimeter measures the distance around it. A helpful pattern to remember: rectangles that are more "square-like" (sides closer in length) have smaller perimeters, while long, skinny rectangles have larger perimeters — even when their areas match. To check, calculate each perimeter using P=2(l+w)P = 2(l + w). Pen A: 2(4+6)=2(10)=202(4 + 6) = 2(10) = 20 feet.
Pen B: 2(3+8)=2(11)=222(3 + 8) = 2(11) = 22 feet. Since 20<2220 < 22, Pen A has a smaller perimeter than Pen B, making B correct. Notice how Pen A (4×64 \times 6) is closer to a square than Pen B (3×83 \times 8), which matches the pattern. Choice A is wrong because equal areas do not guarantee equal perimeters — this is a common misconception. Choice C reverses the correct relationship; it would be true only if Pen A were the more stretched-out shape, but here Pen B is longer and thinner. Choice D is wrong because you already have all the measurements you need — length and width are enough to calculate any rectangle's perimeter. Study tip: Whenever a problem gives you rectangles with the same area but different dimensions, expect the perimeters to differ. The rectangle whose sides are closest to equal (most square-shaped) will always have the smaller perimeter. Practice this by sketching the shapes so you can see the difference, not just calculate it.