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
28 square inches
7 square inches
16 square inches
To find the area of the rectangle within the composite shape, we first need to find the area of the entire composite shape. The composite shape consists of the rectangle and two congruent right triangles.
The area of a triangle can be calculated using the formula: 1/2 * base * height. Given that the height of the triangle is 4 inches and the width is 3 inches, the area of one triangle is 1/2 * 3 * 4 = 6 square inches. Since there are two congruent triangles, the total area contributed by the triangles is 2 * 6 = 12 square inches.
Since the composite shape has an area of 40 square inches and the area contributed by the triangles is 12 square inches, the area of the rectangle within the composite shape is 40 - 12 = 28 square inches.
Therefore, the answer is 28 square inches.