Elementary School Math Quiz: Find Area Of Composite Figures

20 questions · exam conditions

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Find Area Of Composite FiguresQuestion 1 of 20

Look at the shaded region in the figure below. What is the area of the shaded part of this rectangle?

$Question graphic$

45

square inches

39

square inches

51

square inches

33

square inches

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Elementary School Math Quiz

Elementary School Math Quiz: Find Area Of Composite Figures

Practice Find Area Of Composite Figures 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 Find Area Of Composite Figures, 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

Look at the shaded region in the figure below. What is the area of the shaded part of this rectangle?

$45$ square inches
$39$ square inches (correct answer)
$51$ square inches
$33$ square inches

Explanation: The large rectangle is 9 in × 7 in = 63 square inches. The unshaded rectangle in the top right is 4 in × 6 in = 24 square inches. The shaded area = 63 - 24 = 39 square inches.

Question 2

A concrete pad is shaped like a large rectangle with a smaller rectangular section removed from one corner. The large rectangle measures 12 yards by 15 yards. The removed section measures 4 yards by 6 yards.

What is the total area of the concrete pad?

$132$ square yards
$144$ square yards
$156$ square yards (correct answer)
$168$ square yards

Explanation: The large rectangle has an area of 12 times 15, or 180 square yards. The removed section has an area of 4 times 6, or 24 square yards. Subtracting the removed section, 180 minus 24 equals 156 square yards, so C is correct. Choice A (132) subtracts too much area. Choice B (144) does not account for the full removed section. Choice D (168) does not subtract the removed section at all.

Question 3

Look at the floor plan below. Carlos calculated the area by adding $3 \times 4 = 12$ and $2 \times 5 = 10$ to get $22$ square units. His friend Emma calculated it by adding $3 \times 7 = 21$ and $2 \times 1 = 2$ to get $23$ square units. Who is correct and what is the actual area?

Carlos is correct; the actual area is $22$ square units
Emma is correct; the actual area is $23$ square units
Both made errors; the actual area is $21$ square units (correct answer)
Both made errors; the actual area is $20$ square units

Explanation: The correct decomposition is into two rectangles:

3 \times 4 = 12

and

3 \times 3 = 9

, giving

12 + 9 = 21

square units. Carlos used incorrect dimensions for his second rectangle (

2 \times 5

instead of

3 \times 3

). Emma's calculation of

3 \times 7

creates overlap since there is no

7

-unit continuous dimension. Choice A accepts Carlos's error. Choice B accepts Emma's error. Choice D uses yet another incorrect decomposition.

Question 4

Refer to the L-shaped figure. The figure can be split into two rectangles. One rectangle is $8$ feet by $3$ feet, and the other rectangle is $4$ feet by $5$ feet. What is the total area of the figure?

$20$ square feet
$24$ square feet
$44$ square feet (correct answer)
$60$ square feet

Explanation: Area of first rectangle:

8 \times 3 = 24

sq ft. Area of second rectangle:

4 \times 5 = 20

sq ft. Total:

24 + 20 = 44

sq ft. A only counts the second rectangle. B only counts the first. D adds all side lengths incorrectly.

Question 5

Refer to the figure. Two friends measured the same rectilinear shape. Alex broke it into a $5$ ft by $8$ ft rectangle and a $3$ ft by $2$ ft rectangle. What is the total area of the shape?

$18$ square feet
$40$ square feet
$46$ square feet (correct answer)
$48$ square feet

Explanation:

5 \times 8 = 40

and

3 \times 2 = 6

. Total:

40 + 6 = 46

sq ft. B ignores the small rectangle. A adds side lengths. D multiplies wrong numbers.

Question 6

A garden is shaped like the letter T. The top rectangle is $9$ feet by $2$ feet. The bottom rectangle is $3$ feet by $5$ feet. What is the total area of the garden?

$19$ square feet
$27$ square feet
$45$ square feet
$33$ square feet (correct answer)

Explanation: When a shape is made of two rectangles joined together (like a T, L, or plus sign), you can find its total area by finding the area of each rectangle separately and then adding them together. Remember, the area of a rectangle is length × width. Start with the top rectangle:

9 \times 2 = 18

square feet. Then the bottom rectangle:

3 \times 5 = 15

square feet. Add them:

18 + 15 = 33

square feet. That matches choice D. Choice A (

19

) comes from adding the dimensions instead of multiplying — someone did

9+2+3+5=19

, which gives a perimeter-like number, not area. Choice B (

27

) comes from finding only one rectangle's area correctly and mixing up the other; for example,

9+2+3+5+...

or adding

18+9

. Choice C (

45

) is the trap answer — it comes from multiplying

9 \times 5 = 45

, treating the whole T as one big rectangle. But the T shape has empty corners, so it isn't a full

9 \times 5

rectangle. When you see a composite shape (a shape made of more than one rectangle), always break it into separate rectangles, find each area with length × width, then add. Watch out for the trap of multiplying the largest dimensions together as if the shape were one rectangle — that only works for actual rectangles, not for T, L, or plus shapes.

Question 7

Ms. Lee's classroom carpet is shaped like a rectangle with a smaller rectangle attached. The main part is $9$ ft by $6$ ft, and the attached part is $3$ ft by $3$ ft. What is the total area of the carpet?

$63$ square feet (correct answer)
$54$ square feet
$27$ square feet
$72$ square feet

Explanation: When a shape is made from two rectangles joined together, you can find the total area by finding the area of each rectangle separately and then adding them together. Remember, the area of a rectangle is length × width, measured in square units. Start with the main part of the carpet:

9 \times 6 = 54

square feet. Then find the area of the attached part:

3 \times 3 = 9

square feet. Add them together:

54 + 9 = 63

square feet. That matches choice A. Choice B (

54

square feet) is only the area of the main rectangle — it forgets to add the smaller attached piece. Choice C (

27

square feet) comes from adding the side lengths instead of multiplying, or from other addition mistakes with the numbers given; it's far too small for a carpet this size. Choice D (

72

square feet) likely comes from multiplying

9 \times 6

and then adding

3 + 3 + 3 + 3 = 12

(the perimeter of the small square) instead of its area of

9

. When you see a compound shape, always break it into simple rectangles, calculate each area with length × width, then add. Double-check that you multiplied (for area) rather than added the sides (which gives perimeter). Labeling each piece on a quick sketch helps you avoid mixing up the two.

Question 8

Use the figure. A stage is made of two rectangles. The main rectangle is $8$ ft by $4$ ft. A step in front is $6$ ft by $2$ ft. What is the total floor area of the stage and step together?

$20$ square feet
$32$ square feet
$44$ square feet (correct answer)
$48$ square feet

Explanation:

8 \times 4 = 32

and

6 \times 2 = 12

. Total:

32 + 12 = 44

sq ft. B ignores the step. A adds side lengths. D multiplies wrong values.

Question 9

Look at the figure. To find the total area, Kim splits the shape into two rectangles: one is $6$ ft by $3$ ft, and the other is $6$ ft by $2$ ft. What is the total area of the figure?

$17$ square feet
$18$ square feet
$30$ square feet (correct answer)
$36$ square feet

Explanation:

6 \times 3 = 18

and

6 \times 2 = 12

. Total:

18 + 12 = 30

sq ft. B only counts one rectangle. A adds only some sides. D multiplies incorrectly.

Question 10

Refer to the figure. The floor plan of a hallway is made from two rectangles. The long rectangle is $12$ ft by $3$ ft. The shorter rectangle is $4$ ft by $5$ ft. What is the total floor area of the hallway?

$24$ square feet
$36$ square feet
$56$ square feet (correct answer)
$60$ square feet

Explanation:

12 \times 3 = 36

and

4 \times 5 = 20

. Total:

36 + 20 = 56

sq ft. B only counts the long rectangle. A adds the wrong pieces. D multiplies incorrectly.

Question 11

Use the figure. The shape is divided into three non-overlapping rectangles with areas of $14$ sq in, $9$ sq in, and $6$ sq in. What is the total area of the shape?

$15$ square inches
$20$ square inches
$23$ square inches
$29$ square inches (correct answer)

Explanation: Add all three:

14 + 9 + 6 = 29

sq in. A, B, and C each leave out one of the three parts.

Question 12

A school playground is made of two rectangles. The first section measures $5$ yards by $5$ yards. The second section measures $7$ yards by $4$ yards. What is the total area of the playground?

$28$ square yards
$42$ square yards
$53$ square yards (correct answer)
$63$ square yards

Explanation:

5 \times 5 = 25

and

7 \times 4 = 28

. Total:

25 + 28 = 53

sq yd. A only counts the second section. B adds side lengths. D multiplies incorrect values.

Question 13

Refer to the diagram below. Jake is painting this wall that has a rectangular window cut out. What is the area of the wall he needs to paint?

$42$ square feet
$48$ square feet
$54$ square feet (correct answer)
$60$ square feet

Explanation: The total wall area is 8 ft × 9 ft = 72 square feet. The window opening is 3 ft × 6 ft = 18 square feet. The paintable area = 72 - 18 = 54 square feet.

Question 14

Based on the figure shown, Mrs. Johnson needs to find the area of this swimming pool deck. The deck has an unusual shape. What is the total area?

$120$ square meters
$108$ square meters (correct answer)
$132$ square meters
$114$ square meters

Explanation: The deck can be divided into two rectangles. The larger rectangle is 10 m × 8 m = 80 square meters. The smaller attached rectangle is 7 m × 4 m = 28 square meters. Total area = 80 + 28 = 108 square meters.

Question 15

Use the figure shown to answer this question. Anna wants to carpet this T-shaped room. What is the total area she needs to cover?

$96$ square feet
$88$ square feet (correct answer)
$104$ square feet
$92$ square feet

Explanation: The T-shaped room can be split into two rectangles. The horizontal top section is 12 ft × 4 ft = 48 square feet. The vertical bottom section is 5 ft × 8 ft = 40 square feet. Total area = 48 + 40 = 88 square feet.

Question 16

Sarah wants to install new flooring in an L-shaped room. The room can be split into two rectangles: one measuring 10 feet by 10 feet, and another measuring 6 feet by 3 feet. What is the total floor area?

$126$ square feet
$134$ square feet
$118$ square feet (correct answer)
$142$ square feet

Explanation: The first rectangle has an area of 10 times 10, or 100 square feet, and the second has an area of 6 times 3, or 18 square feet. Adding these gives 100 plus 18, which is 118 square feet total. Choice A, 126 square feet, Choice B, 134 square feet, and Choice D, 142 square feet, all come from errors in multiplying or adding the two rectangle areas.

Question 17

A patio is shaped like an L. It can be split into a $7$ m by $4$ m rectangle and a $2$ m by $3$ m rectangle. Which expression could be used to find the total area of the patio in square meters?

$(7+4) + (2+3)$
$(7 \times 4) + (2 \times 3)$ (correct answer)
$(7 \times 4) - (2 \times 3)$
$(7 \times 2) + (4 \times 3)$

Explanation: When a shape is irregular, like an L-shape, a helpful strategy is to split it into rectangles you already know how to handle, find the area of each piece, and then add those areas together. Remember: the area of a rectangle is found by multiplying length by width, not adding them. Here, the patio splits into two rectangles. The first is

7

m by

4

m, so its area is

7 \times 4 = 28

square meters. The second is

2

m by

3

m, so its area is

2 \times 3 = 6

square meters. Adding those together gives the total area:

(7 \times 4) + (2 \times 3) = 34

square meters. That matches choice B. Choice A adds the side lengths instead of multiplying them — that would give you a perimeter-style calculation, not area. Choice C subtracts the smaller rectangle's area, which you'd only do if you were cutting a piece out of a larger rectangle, not combining two separate pieces. Choice D multiplies mismatched sides (a length from one rectangle with a width from the other), which doesn't represent either rectangle's actual area. A good tip: whenever you see "area," your brain should immediately think "multiply length × width." Whenever you see "perimeter," think "add up all the sides." Mixing these two up is one of the most common traps on geometry questions, so pause and ask yourself which one the problem is really asking for before you pick your operation.

Question 18

A rectangular pool deck is made of two parts. The swimming area is $10$ m by $5$ m, and the wading area is $4$ m by $4$ m. If both parts are covered with tile, how many square meters of tile are needed?

$66$ square meters (correct answer)
$50$ square meters
$23$ square meters
$80$ square meters

Explanation: When a shape is made up of two separate rectangles, you can find the total area by calculating the area of each rectangle and then adding them together. The area of a rectangle is length × width, measured in square units. Start with the swimming area:

10 \text{ m} \times 5 \text{ m} = 50

square meters. Then the wading area:

4 \text{ m} \times 4 \text{ m} = 16

square meters. Add the two areas together:

50 + 16 = 66

square meters. That matches choice A. Choice B (

50

) is only the swimming area — it forgets to include the wading area entirely. Choice C (

23

) comes from adding the side lengths instead of multiplying them (

10 + 5 + 4 + 4 = 23

), which confuses perimeter-style addition with area. Choice D (

80

) comes from multiplying the two areas' dimensions incorrectly, like doing

10 \times 4 \times 2 = 80

or a similar mix-up — a trap when you rush and combine numbers without thinking about what each represents. A helpful strategy: when a problem describes two shapes, underline each one separately and calculate its area before combining. Remember, area uses multiplication (length × width) and is always in square units, while perimeter uses addition. Getting these two ideas mixed up is the most common trap on area questions.

Question 19

Use the figure to answer the question. The rectilinear figure is made from two non-overlapping rectangles. Rectangle A measures $7$ cm by $2$ cm and Rectangle B measures $3$ cm by $6$ cm. What is the area of the whole figure?

$18$ square centimeters
$26$ square centimeters
$32$ square centimeters (correct answer)
$36$ square centimeters

Explanation:

7 \times 2 = 14

and

3 \times 6 = 18

. Total:

14 + 18 = 32

sq cm. A is only Rectangle B. B is the perimeter-like sum. D adds a small extra piece.

Question 20

Maya's L-shaped garden can be split into two rectangles: one measuring 6 feet by 5 feet, and another measuring 3 feet by 6 feet. What is the total area of the garden?

$48$ square feet (correct answer)
$52$ square feet
$44$ square feet
$40$ square feet

Explanation: The first rectangle has an area of 6 times 5, or 30 square feet, and the second has an area of 3 times 6, or 18 square feet. Adding these gives 30 plus 18, which is 48 square feet total. Choice B, 52 square feet, Choice C, 44 square feet, and Choice D, 40 square feet, all come from errors in multiplying or adding the two rectangle areas.