Find Area of Composite Figures
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3rd Grade Math › Find Area of Composite Figures
Look at the shaded region in the figure below. What is the area of the shaded part of this rectangle?

$$51$$ 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.
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?

$$156$$ 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.
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
$$104$$ 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.
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
$$54$$ 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.
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?

$$44$$ 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.
Look at this floor plan diagram. Sarah wants to install new flooring in this oddly-shaped room. What is the total floor area?

$$142$$ 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.
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?

$$108$$ 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.