Area of Composite Figures Quick Check
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Question
Use the image to answer the question.
A composite figure is comprised of a rectangle and two congruent right triangle on either side. The triangle have a height of 4 inches and a width of 3 inches.
The composite shape in the image has an area of 40 square inches. What is the area of the rectangle within the composite shape?
First, let's find the area of each triangle.
Each triangle has a height of 4 inches and a base of 3 inches. The area formula for a triangle is A = 1/2 * base * height.
For one triangle:
A = 1/2 * 3 * 4
A = 1/2 * 12
A = 6 square inches
Since there are two congruent triangles, the total area of the triangles is 2 * 6 = 12 square inches.
Now, to find the area of the rectangle within the composite shape, we need to subtract the total area of the triangles from the total area of the composite shape.
Total area of the composite shape = 40 square inches
Total area of the triangles = 12 square inches
Area of the rectangle = Total area of the composite shape - Total area of the triangles
Area of the rectangle = 40 - 12
Area of the rectangle = 28 square inches
Therefore, the area of the rectangle within the composite shape is 28 square inches.