Elementary School Math Quiz: Use Area Models For Distribution
20 questions · exam conditions
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Use Area Models For DistributionQuestion 1 of 20

Maya's rectangular floor has a length of 5 units and a width of (4+4)(4+4) units. What is the total area of the floor, in square units?

40 square units
45 square units
20 square units
25 square units
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Elementary School Math Quiz

Elementary School Math Quiz: Use Area Models For Distribution

Practice Use Area Models For Distribution 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 Use Area Models For Distribution, 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

Maya's rectangular floor has a length of 5 units and a width of (4+4)(4+4) units. What is the total area of the floor, in square units?

  1. 40 square units (correct answer)
  2. 45 square units
  3. 20 square units
  4. 25 square units
Explanation: The floor's width is 4+4=8 units, so the area is 5 x 8 = 40 square units, making Choice A correct. Choice B (45) adds an extra unit that isn't part of either dimension. Choice C (20) uses only one of the 4's instead of adding them together first. Choice D (25) comes from treating the width as 5 instead of 8.

Question 2

A hallway is 6 feet wide. It is divided into two sections: one section is 4 feet long and the other is 3 feet long. What is the total area of the hallway?

  1. 27 square feet
  2. 18 square feet
  3. 24 square feet
  4. 42 square feet (correct answer)
Explanation: The total length is 4 feet plus 3 feet, or 7 feet, and area equals length times width, so 7 times 6 equals 42 square feet. Choice A comes from a miscalculation of the total length. Choice B only uses one section's length instead of the full hallway. Choice C comes from multiplying the width by only part of the length.

Question 3

A rectangular playground has an area that can be calculated as 8×(5+2)8 \times (5 + 2). If the playground is divided into a basketball court and a sandbox, and the basketball court has area 8×58 \times 5, what is the area of the sandbox?

  1. 8×7=56 square units8 \times 7 = 56 \text{ square units}
  2. 8+2=10 square units8 + 2 = 10 \text{ square units}
  3. 5×2=10 square units5 \times 2 = 10 \text{ square units}
  4. 8×2=16 square units8 \times 2 = 16 \text{ square units} (correct answer)
Explanation: When you see a problem about breaking apart areas, think about how the distributive property works with multiplication. The total playground area is 8×(5+2)8 \times (5 + 2), which means the playground is 8 units wide and has a total length of (5+2)=7(5 + 2) = 7 units. Since the basketball court takes up 8×58 \times 5 square units of the total area, you can find the sandbox area by using the distributive property. When you distribute the 8, you get: 8×(5+2)=(8×5)+(8×2)8 \times (5 + 2) = (8 \times 5) + (8 \times 2). The basketball court is 8×58 \times 5, so the remaining piece—the sandbox—must be 8×2=168 \times 2 = 16 square units. Looking at the wrong answers: Choice A calculates 8×7=568 \times 7 = 56, which is actually the total playground area, not just the sandbox. Choice B gives 8+2=108 + 2 = 10, which incorrectly adds instead of multiplying—remember, area always involves multiplication of length and width. Choice C calculates 5×2=105 \times 2 = 10, which uses the wrong dimensions and ignores that the sandbox shares the 8-unit width with the basketball court. The correct answer is D: 8×2=168 \times 2 = 16 square units. Remember this pattern: when you see an area problem with parts, use the distributive property. If the total area is length times (a+b)(a + b), then the two parts have areas of length times aa and length times bb.

Question 4

Lisa is using unit squares to tile two connected rectangular sections of her classroom floor. The first section is 5 squares wide and 3 squares long. The second section is 5 squares wide and 4 squares long. They share the same width. How many unit squares does she need in total?

  1. 5×(3+4)=35 squares5 \times (3 + 4) = 35 \text{ squares} (correct answer)
  2. (5+3)×(5+4)=72 squares(5 + 3) \times (5 + 4) = 72 \text{ squares}
  3. 5+3+5+4=17 squares5 + 3 + 5 + 4 = 17 \text{ squares}
  4. 5×3×5×4=300 squares5 \times 3 \times 5 \times 4 = 300 \text{ squares}
Explanation: Since both sections have the same width (5), we can use the distributive property: 5×3+5×4=5×(3+4)=5×7=355 \times 3 + 5 \times 4 = 5 \times (3 + 4) = 5 \times 7 = 35. Choice B incorrectly adds dimensions, choice C adds perimeter instead of finding area, and choice D multiplies all dimensions together.

Question 5

A rectangle is 8 units wide and 5 units tall. Elena splits the 8 into two parts to divide the rectangle into two smaller rectangles.

If Elena splits the width of 8 into 3 and 5, which equation correctly shows the split of the rectangle's area?

  1. 5×8=5×3+5×55 \times 8 = 5 \times 3 + 5 \times 5 (correct answer)
  2. 5×8=5×4+5×55 \times 8 = 5 \times 4 + 5 \times 5
  3. 5×8=5×3+5×65 \times 8 = 5 \times 3 + 5 \times 6
  4. 5×8=5×2+5×55 \times 8 = 5 \times 2 + 5 \times 5
Explanation: Since 3 plus 5 equals 8, splitting the width into 3 and 5 correctly matches the original rectangle. Choice B splits the width into 4 and 5, which adds up to 9, not 8. Choice C splits the width into 3 and 6, which adds up to 9, not 8. Choice D splits the width into 2 and 5, which adds up to 7, not 8.

Question 6

Tommy is tiling a rectangular garden bed that is 6 feet by 8 feet. The two non-overlapping sections that together cover the entire garden are a 6-by-5 section for flowers and a 6-by-3 section for vegetables. If each square foot needs one tile, which expression represents the total number of tiles he needs?

  1. 6×5+6×36 \times 5 + 6 \times 3 (correct answer)
  2. 6+5×6+36 + 5 \times 6 + 3
  3. 6×(5+3)×26 \times (5 + 3) \times 2
  4. 6×8−(5+3)6 \times 8 - (5 + 3)
Explanation: The correct expression is A) 6x5 + 6x3, which adds the tile counts for the two sections (30 for flowers, 18 for vegetables) since together they cover the whole 6-by-8 garden. Choice B misuses order of operations, mixing addition and multiplication in a way that doesn't represent either section correctly. Choice C doubles the total unnecessarily. Choice D subtracts the section widths from the total area instead of adding the two section areas, which doesn't correctly represent tiling both sections.

Question 7

A rectangle is 5 units by 8 units. It is split into two smaller rectangles: one 5 by 2 and the other 5 by 6. What is the total area of the original rectangle?

  1. 30 square units
  2. 60 square units
  3. 10 square units
  4. 40 square units (correct answer)
Explanation: The two smaller rectangles have areas of 5 times 2, or 10, and 5 times 6, or 30, which add up to 40 square units total. Choice A is only the area of the larger part. Choice B comes from multiplying the two given lengths, 5 times 6 by 2 instead of adding the two areas. Choice C is only the area of the smaller part.

Question 8

A rectangle is made up of two sections: one section measures 2 units by 5 units, and the other section measures 2 units by 4 units. What is the total area of the rectangle?

  1. 9 square units
  2. 18 square units (correct answer)
  3. 14 square units
  4. 40 square units
Explanation: The first section has an area of 2 x 5 = 10 square units, and the second has an area of 2 x 4 = 8 square units. Adding these gives 10 + 8 = 18 square units total, so Choice B is correct. Choices A and C come from adding or combining the dimensions instead of finding each section's area first. Choice D treats the shape as one rectangle with all four numbers multiplied together, which does not match how the shape is actually divided.

Question 9

Jamal's garden is 4 meters wide. Its length is made up of two sections: 3 meters and 2 meters. What is the total area?

  1. 24 square meters
  2. 20 square meters (correct answer)
  3. 12 square meters
  4. 14 square meters
Explanation: The total length is 3 plus 2, or 5 meters, and area equals length times width, so 4 times 5 equals 20 square meters. Choice A comes from a multiplication error. Choice C only uses one of the two length sections. Choice D comes from adding instead of multiplying the dimensions.

Question 10

Sofia's poster is 3 inches wide and 7 inches tall, divided into a 5-inch-tall section and a 2-inch-tall section. What is the total area of the poster?

  1. 13 square inches
  2. 15 square inches
  3. 17 square inches
  4. 21 square inches (correct answer)
Explanation: The poster is 3 inches wide and 7 inches tall in total, so the area is 3 times 7, which is 21 square inches, matching choice D. This also matches adding the two sections separately: 3 times 5, plus 3 times 2, which is 15 plus 6, or 21. Choices A, B, and C come from using only part of the poster's height or miscalculating the sections.

Question 11

Keisha's garden has a width of 3 units. Its length is split into two parts: 4 units and 2 units. What is the total area of the garden, in square units?

  1. 18 square units (correct answer)
  2. 24 square units
  3. 14 square units
  4. 12 square units
Explanation: Keisha's garden has a width of 3 units, split into length parts of 4 and 2 units, for a total length of 6 units. The area is 3 times 6, which equals 18 square units, so A is correct. Choice B (24) does not match multiplying 3 by 6. Choice C (14) is close to but not equal to the correct product. Choice D (12) only accounts for one of the two length parts.

Question 12

A rectangle is 4 units wide. Its length is split into two parts: 3 units and 2 units. What is the total area?

  1. 12 square units
  2. 20 square units (correct answer)
  3. 24 square units
  4. 14 square units
Explanation: The total length is 3 plus 2, or 5 units, and area equals length times width, so 4 times 5 equals 20 square units. Choice A only uses one of the two length parts. Choice C comes from a multiplication error. Choice D comes from adding instead of multiplying the dimensions.

Question 13

A rectangle is divided into two sections along its length. One section is 5 units long and the other is 3 units long, and the rectangle is 4 units wide. What is the total area in square units?

  1. 32 square units (correct answer)
  2. 20 square units
  3. 28 square units
  4. 60 square units
Explanation: Adding the two lengths, 5 plus 3, gives 8 units total, and 4 times 8 equals 32 square units. Choice B (20) only counts the area of one section instead of both. Choice C (28) comes from an incorrect total length before multiplying. Choice D (60) comes from multiplying the two section lengths together instead of adding them.

Question 14

Sophie draws a rectangle to show that 4×9=4×(6+3)4 \times 9 = 4 \times (6 + 3). The rectangle is 4 units wide. She splits the 9-unit length into two parts: one part is 6 units long, and the other part is 3 units long. What is the area of the smaller part?

  1. 6×3=18 square units6 \times 3 = 18 \text{ square units}
  2. 4+3=7 square units4 + 3 = 7 \text{ square units}
  3. 4×3=12 square units4 \times 3 = 12 \text{ square units} (correct answer)
  4. 4×6=24 square units4 \times 6 = 24 \text{ square units}
Explanation: The smaller part is 3 units long, and the rectangle is 4 units wide, so its area is 4 times 3, which is 12 square units. Choice A, 6 times 3, uses the wrong length for this part. Choice B, 4 plus 3, adds the dimensions instead of multiplying them. Choice D, 4 times 6, gives the area of the larger part instead of the smaller one.

Question 15

This area model is 33 by (5+1)(5+1). What is the total area?

  1. 16 square units
  2. 18 square units (correct answer)
  3. 12 square units
  4. 15 square units
Explanation: 18 square units is correct because 3 times 6 equals 18. 16 square units is incorrect because it does not match the correct product. 12 square units is incorrect because it does not match multiplying 3 by 6. 15 square units is incorrect because it uses only the 5 and skips adding the 1 before multiplying.

Question 16

A rectangle is 3 units wide and 6 units long. The 6-unit length is split into two parts: 2 units and 4 units. Which equation uses the distributive property to find the total area?

  1. 3×(2+4)=3×2+3×43 \times (2 + 4) = 3 \times 2 + 3 \times 4 (correct answer)
  2. 3×6=2×4+3×23 \times 6 = 2 \times 4 + 3 \times 2
  3. (3+2)×(3+4)=3×2+3×4(3 + 2) \times (3 + 4) = 3 \times 2 + 3 \times 4
  4. 3×6=3+2+3+43 \times 6 = 3 + 2 + 3 + 4
Explanation: The rectangle's area can be split into two smaller rectangles: 3 by 2 and 3 by 4, so 3 times (2 plus 4) equals 3 times 2 plus 3 times 4. Choice B mixes up which numbers get multiplied and added. Choice C incorrectly adds the widths and lengths together before multiplying. Choice D confuses multiplication with simple addition of all the parts.

Question 17

Look at the rectangle shown. Maya wants to find the total area by breaking it into two smaller rectangles. Which equation shows how the distributive property applies to this area model?

  1. 4×(3+2)=(4×3)+(4×2)4 \times (3 + 2) = (4 \times 3) + (4 \times 2) (correct answer)
  2. 4×(3+2)=(4+3)×(4+2)4 \times (3 + 2) = (4 + 3) \times (4 + 2)
  3. 4×(3+2)=(4×3)×(4×2)4 \times (3 + 2) = (4 \times 3) \times (4 \times 2)
  4. 4×(3+2)=4+(3×2)4 \times (3 + 2) = 4 + (3 \times 2)
Explanation: The distributive property states that multiplying a number by a sum equals the sum of multiplying that number by each addend separately. Here, 4×(3+2)=(4×3)+(4×2)4 \times (3 + 2) = (4 \times 3) + (4 \times 2). Choice B incorrectly distributes to both factors, choice C uses multiplication instead of addition, and choice D doesn't properly distribute the 4.

Question 18

Study the area model diagram. Marcus wants to verify that his area calculation is correct by using the distributive property. Which statement about this rectangle is true?

  1. The total area equals 6×3+6×4=42 square units6 \times 3 + 6 \times 4 = 42 \text{ square units} (correct answer)
  2. The total area equals 6+3+6+4=19 square units6 + 3 + 6 + 4 = 19 \text{ square units}
  3. The total area equals 6×7−3×4=30 square units6 \times 7 - 3 \times 4 = 30 \text{ square units}
  4. The total area equals 3×4+6×2=24 square units3 \times 4 + 6 \times 2 = 24 \text{ square units}
Explanation: The rectangle shows width 6 with length divided into sections of 3 and 4. Using the distributive property: 6×(3+4)=6×3+6×4=18+24=426 \times (3 + 4) = 6 \times 3 + 6 \times 4 = 18 + 24 = 42. Choice B finds perimeter, choice C incorrectly subtracts areas, and choice D uses wrong dimensions.

Question 19

A rectangle is 3 units wide. Its length is split into two parts: 4 units and 2 units. What is the total area?

  1. 18 square units (correct answer)
  2. 24 square units
  3. 20 square units
  4. 12 square units
Explanation: The total length is 4 plus 2, or 6 units, and area equals length times width, so 3 times 6 equals 18 square units. Choice B comes from a multiplication error. Choice C comes from adding instead of multiplying the dimensions. Choice D only uses one of the two length parts.

Question 20

A rectangle has a width of 7 units. Its length is split into two parts: one part is 4 units, and the other part is unknown. The total area of the rectangle is 70 square units. What is the missing length?

  1. 6 (correct answer)
  2. 10
  3. 2
  4. 4
Explanation: The total area is 70 square units, and the width is 7, so the total length is 70 divided by 7, which is 10. Since one part of the length is 4, the missing part is 10 minus 4, or 6, so A is correct. Choice B (10) is the total length, not just the missing part. Choice C (2) is too small to complete the total length correctly. Choice D (4) repeats the known part instead of finding the missing one.