What is the area of the shape?
Understand the Problem
The question asks us to find the area of the shape. We can calculate the area by calculating the area of the outer rectangle, and subtracting the area of the inner rectangle.
Answer
$131 \text{ ft}^2$
Answer for screen readers
$131 \text{ ft}^2$
Steps to Solve
- Calculate the area of the outer rectangle
The outer rectangle has sides of 17 ft and 4+7 = 11 ft. The area is calculated as:
$$Area_{outer} = length \times width = 17 \times 11$$
- Compute the area of the outer rectangle
$$Area_{outer} = 17 \times 11 = 187 \text{ ft}^2 $$
- Calculate the area of the inner rectangle
The inner rectangle has sides of 8 ft and 7 ft. The area is calculated as:
$$Area_{inner} = length \times width = 8 \times 7$$
- Compute the area of the inner rectangle
$$Area_{inner} = 8 \times 7 = 56 \text{ ft}^2$$
- Calculate the area of the shape
The area of the shape is the area of the outer rectangle minus the area of the inner rectangle:
$$Area_{shape} = Area_{outer} - Area_{inner} = 187 - 56$$
- Compute the area of the shape
$$Area_{shape} = 187 - 56 = 131 \text{ ft}^2$$
$131 \text{ ft}^2$
More Information
The area of the shape is $131 \text{ ft}^2$.
Tips
A common mistake is to add the area of the inner rectangle to the area of the outer rectangle. Another common mistake is to miscalculate the sides of the rectangles.
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