3rd Grade Math Quiz: Find Area Of Composite Figures
20 questions · exam conditions
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Find Area Of Composite FiguresQuestion 1 of 20

A rectangular rug is 88 feet by 66 feet. A smaller rectangular rug that is 44 feet by 33 feet is placed next to it, not overlapping. What is the combined area of both rugs?

2121 square feet
6060 square feet
4848 square feet
7272 square feet
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3rd Grade Math Quiz

3rd Grade Math Quiz: Find Area Of Composite Figures

Practice Find Area Of Composite Figures in 3rd Grade 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 3rd Grade 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

A rectangular rug is 88 feet by 66 feet. A smaller rectangular rug that is 44 feet by 33 feet is placed next to it, not overlapping. What is the combined area of both rugs?

  1. 2121 square feet
  2. 6060 square feet (correct answer)
  3. 4848 square feet
  4. 7272 square feet
Explanation: When you're asked to find the combined area of two shapes, the strategy is simple: find each area separately, then add them together. The area of a rectangle is found by multiplying length × width. Start with the larger rug: 8×6=488 \times 6 = 48 square feet. Then the smaller rug: 4×3=124 \times 3 = 12 square feet. Adding these together gives 48+12=6048 + 12 = 60 square feet, which matches choice B. Choice A (2121) comes from adding the dimensions instead of multiplying them: 8+6+4+3=218 + 6 + 4 + 3 = 21. That's a perimeter-style mistake, not an area calculation. Choice C (4848) is only the area of the larger rug — it forgets to include the smaller rug entirely. Choice D (7272) comes from multiplying all four numbers together in a mixed-up way (for example, 8×3×3=728 \times 3 \times 3 = 72 or similar errors), which doesn't represent either rug's area correctly. A helpful tip: whenever a problem says "combined," "total," or "altogether" with shapes, treat it as a two-step problem — calculate each area first, then add. Also, remember the difference between area (multiply length × width, answer in square units) and perimeter (add all sides, answer in regular units). Mixing these up is one of the most common traps in geometry questions.

Question 2

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

  1. 4545 square inches
  2. 3939 square inches (correct answer)
  3. 5151 square inches
  4. 3333 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 3

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?

  1. 132132 square yards
  2. 144144 square yards
  3. 156156 square yards (correct answer)
  4. 168168 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 4

Look at the floor plan below. Carlos calculated the area by adding 3×4=123 \times 4 = 12 and 2×5=102 \times 5 = 10 to get 2222 square units. His friend Emma calculated it by adding 3×7=213 \times 7 = 21 and 2×1=22 \times 1 = 2 to get 2323 square units. Who is correct and what is the actual area?

  1. Carlos is correct; the actual area is 2222 square units
  2. Emma is correct; the actual area is 2323 square units
  3. Both made errors; the actual area is 2121 square units (correct answer)
  4. Both made errors; the actual area is 2020 square units
Explanation: The correct decomposition is into two rectangles: 3×4=123 \times 4 = 12 and 3×3=93 \times 3 = 9, giving 12+9=2112 + 9 = 21 square units. Carlos used incorrect dimensions for his second rectangle (2×52 \times 5 instead of 3×33 \times 3). Emma's calculation of 3×73 \times 7 creates overlap since there is no 77-unit continuous dimension. Choice A accepts Carlos's error. Choice B accepts Emma's error. Choice D uses yet another incorrect decomposition.

Question 5

Refer to the L-shaped figure. The figure can be split into two rectangles. One rectangle is 88 feet by 33 feet, and the other rectangle is 44 feet by 55 feet. What is the total area of the figure?

  1. 2020 square feet
  2. 2424 square feet
  3. 4444 square feet (correct answer)
  4. 6060 square feet
Explanation: Area of first rectangle: 8×3=248 \times 3 = 24 sq ft. Area of second rectangle: 4×5=204 \times 5 = 20 sq ft. Total: 24+20=4424 + 20 = 44 sq ft. A only counts the second rectangle. B only counts the first. D adds all side lengths incorrectly.

Question 6

Refer to the figure. Two friends measured the same rectilinear shape. Alex broke it into a 55 ft by 88 ft rectangle and a 33 ft by 22 ft rectangle. What is the total area of the shape?

  1. 1818 square feet
  2. 4040 square feet
  3. 4646 square feet (correct answer)
  4. 4848 square feet
Explanation: 5×8=405 \times 8 = 40 and 3×2=63 \times 2 = 6. Total: 40+6=4640 + 6 = 46 sq ft. B ignores the small rectangle. A adds side lengths. D multiplies wrong numbers.

Question 7

A garden is shaped like the letter T. The top rectangle is 99 feet by 22 feet. The bottom rectangle is 33 feet by 55 feet. What is the total area of the garden?

  1. 1919 square feet
  2. 2727 square feet
  3. 4545 square feet
  4. 3333 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: 9×2=189 \times 2 = 18 square feet. Then the bottom rectangle: 3×5=153 \times 5 = 15 square feet. Add them: 18+15=3318 + 15 = 33 square feet. That matches choice D. Choice A (1919) comes from adding the dimensions instead of multiplying — someone did 9+2+3+5=199+2+3+5=19, which gives a perimeter-like number, not area. Choice B (2727) comes from finding only one rectangle's area correctly and mixing up the other; for example, 9+2+3+5+...9+2+3+5+... or adding 18+918+9. Choice C (4545) is the trap answer — it comes from multiplying 9×5=459 \times 5 = 45, treating the whole T as one big rectangle. But the T shape has empty corners, so it isn't a full 9×59 \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 8

Ms. Lee's classroom carpet is shaped like a rectangle with a smaller rectangle attached. The main part is 99 ft by 66 ft, and the attached part is 33 ft by 33 ft. What is the total area of the carpet?

  1. 6363 square feet (correct answer)
  2. 5454 square feet
  3. 2727 square feet
  4. 7272 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: 9×6=549 \times 6 = 54 square feet. Then find the area of the attached part: 3×3=93 \times 3 = 9 square feet. Add them together: 54+9=6354 + 9 = 63 square feet. That matches choice A. Choice B (5454 square feet) is only the area of the main rectangle — it forgets to add the smaller attached piece. Choice C (2727 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 (7272 square feet) likely comes from multiplying 9×69 \times 6 and then adding 3+3+3+3=123 + 3 + 3 + 3 = 12 (the perimeter of the small square) instead of its area of 99. 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 9

Use the figure. A stage is made of two rectangles. The main rectangle is 88 ft by 44 ft. A step in front is 66 ft by 22 ft. What is the total floor area of the stage and step together?

  1. 2020 square feet
  2. 3232 square feet
  3. 4444 square feet (correct answer)
  4. 4848 square feet
Explanation: 8×4=328 \times 4 = 32 and 6×2=126 \times 2 = 12. Total: 32+12=4432 + 12 = 44 sq ft. B ignores the step. A adds side lengths. D multiplies wrong values.

Question 10

Look at the figure. To find the total area, Kim splits the shape into two rectangles: one is 66 ft by 33 ft, and the other is 66 ft by 22 ft. What is the total area of the figure?

  1. 1717 square feet
  2. 1818 square feet
  3. 3030 square feet (correct answer)
  4. 3636 square feet
Explanation: 6×3=186 \times 3 = 18 and 6×2=126 \times 2 = 12. Total: 18+12=3018 + 12 = 30 sq ft. B only counts one rectangle. A adds only some sides. D multiplies incorrectly.

Question 11

Refer to the figure. The floor plan of a hallway is made from two rectangles. The long rectangle is 1212 ft by 33 ft. The shorter rectangle is 44 ft by 55 ft. What is the total floor area of the hallway?

  1. 2424 square feet
  2. 3636 square feet
  3. 5656 square feet (correct answer)
  4. 6060 square feet
Explanation: 12×3=3612 \times 3 = 36 and 4×5=204 \times 5 = 20. Total: 36+20=5636 + 20 = 56 sq ft. B only counts the long rectangle. A adds the wrong pieces. D multiplies incorrectly.

Question 12

Use the figure. The shape is divided into three non-overlapping rectangles with areas of 1414 sq in, 99 sq in, and 66 sq in. What is the total area of the shape?

  1. 1515 square inches
  2. 2020 square inches
  3. 2323 square inches
  4. 2929 square inches (correct answer)
Explanation: Add all three: 14+9+6=2914 + 9 + 6 = 29 sq in. A, B, and C each leave out one of the three parts.

Question 13

A school playground is made of two rectangles. The first section measures 55 yards by 55 yards. The second section measures 77 yards by 44 yards. What is the total area of the playground?

  1. 2828 square yards
  2. 4242 square yards
  3. 5353 square yards (correct answer)
  4. 6363 square yards
Explanation: 5×5=255 \times 5 = 25 and 7×4=287 \times 4 = 28. Total: 25+28=5325 + 28 = 53 sq yd. A only counts the second section. B adds side lengths. D multiplies incorrect values.

Question 14

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?

  1. 4242 square feet
  2. 4848 square feet
  3. 5454 square feet (correct answer)
  4. 6060 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 15

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?

  1. 120120 square meters
  2. 108108 square meters (correct answer)
  3. 132132 square meters
  4. 114114 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 16

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?

  1. 9696 square feet
  2. 8888 square feet (correct answer)
  3. 104104 square feet
  4. 9292 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 17

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?

  1. 126126 square feet
  2. 134134 square feet
  3. 118118 square feet (correct answer)
  4. 142142 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 18

A patio is shaped like an L. It can be split into a 77 m by 44 m rectangle and a 22 m by 33 m rectangle. Which expression could be used to find the total area of the patio in square meters?

  1. (7+4)+(2+3)(7+4) + (2+3)
  2. (7×4)+(2×3)(7 \times 4) + (2 \times 3) (correct answer)
  3. (7×4)−(2×3)(7 \times 4) - (2 \times 3)
  4. (7×2)+(4×3)(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 77 m by 44 m, so its area is 7×4=287 \times 4 = 28 square meters. The second is 22 m by 33 m, so its area is 2×3=62 \times 3 = 6 square meters. Adding those together gives the total area: (7×4)+(2×3)=34(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 19

A rectangular pool deck is made of two parts. The swimming area is 1010 m by 55 m, and the wading area is 44 m by 44 m. If both parts are covered with tile, how many square meters of tile are needed?

  1. 6666 square meters (correct answer)
  2. 5050 square meters
  3. 2323 square meters
  4. 8080 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 m×5 m=5010 \text{ m} \times 5 \text{ m} = 50 square meters. Then the wading area: 4 m×4 m=164 \text{ m} \times 4 \text{ m} = 16 square meters. Add the two areas together: 50+16=6650 + 16 = 66 square meters. That matches choice A. Choice B (5050) is only the swimming area — it forgets to include the wading area entirely. Choice C (2323) comes from adding the side lengths instead of multiplying them (10+5+4+4=2310 + 5 + 4 + 4 = 23), which confuses perimeter-style addition with area. Choice D (8080) comes from multiplying the two areas' dimensions incorrectly, like doing 10×4×2=8010 \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 20

Use the figure to answer the question. The rectilinear figure is made from two non-overlapping rectangles. Rectangle A measures 77 cm by 22 cm and Rectangle B measures 33 cm by 66 cm. What is the area of the whole figure?

  1. 1818 square centimeters
  2. 2626 square centimeters
  3. 3232 square centimeters (correct answer)
  4. 3636 square centimeters
Explanation: 7×2=147 \times 2 = 14 and 3×6=183 \times 6 = 18. Total: 14+18=3214 + 18 = 32 sq cm. A is only Rectangle B. B is the perimeter-like sum. D adds a small extra piece.