Find Area of Composite Figures

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3rd Grade Math › Find Area of Composite Figures

Questions 1 - 7
1

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

Question graphic

$$51$$ square inches

$$39$$ square inches

$$45$$ 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.

2

Use the figure shown below to solve this problem. A builder needs to calculate the area of this concrete pad. What is the total area?

Question graphic

$$156$$ square yards

$$144$$ square yards

$$168$$ square yards

$$132$$ square yards

Explanation

The concrete pad forms an L-shape that can be split into two rectangles. The vertical rectangle is 6 yd × 18 yd = 108 square yards. The horizontal rectangle is 8 yd × 6 yd = 48 square yards. Total area = 108 + 48 = 156 square yards.

3

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?

Question graphic

$$96$$ square feet

$$104$$ square feet

$$92$$ square feet

$$88$$ 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.

4

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?

Question graphic

$$42$$ square feet

$$54$$ square feet

$$48$$ square feet

$$60$$ 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.

5

Look at the figure below. Maya wants to find the total area of this L-shaped garden. She breaks it into two rectangles. What is the total area of the garden?

Question graphic

$$44$$ square feet

$$52$$ square feet

$$40$$ square feet

$$48$$ square feet

Explanation

The L-shaped figure can be decomposed into two rectangles. The top rectangle is 8 ft × 4 ft = 32 square feet. The bottom rectangle is 4 ft × 4 ft = 16 square feet. Total area = 32 + 16 = 48 square feet.

6

Look at this floor plan diagram. Sarah wants to install new flooring in this oddly-shaped room. What is the total floor area?

Question graphic

$$142$$ square feet

$$126$$ square feet

$$118$$ square feet

$$134$$ square feet

Explanation

The room can be divided into three rectangles. Top rectangle: 8 ft × 5 ft = 40 sq ft. Middle rectangle: 6 ft × 7 ft = 42 sq ft. Bottom rectangle: 9 ft × 4 ft = 36 sq ft. Total: 40 + 42 + 36 = 118 square feet.

7

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?

Question graphic

$$108$$ square meters

$$132$$ square meters

$$114$$ square meters

$$120$$ 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.