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?

(1 point)
Responses

34 square inches
34 square inches

7 square inches
7 square inches

28 square inches
28 square inches

16 square inches
16 square inches
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Answer 1

The area of the composite figure is equal to the sum of the areas of the rectangle and the two congruent triangles.

Area of one triangle = (1/2) x base x height = (1/2) x 3 x 4 = 6 square inches.
Since there are two triangles in the composite figure, the total area of the triangles is 2 x 6 = 12 square inches.

The total area of the composite figure is 40 square inches.
Therefore, the area of the rectangle = Total area - Total area of triangles = 40 - 12 = 28 square inches.

So, the correct answer is:
28 square inches