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? please explain step by step
To find the area of the rectangle within the composite shape, we first need to find the total area of the composite shape and then subtract the areas of the two triangles.
1. Area of each triangle:
Since the two triangles are congruent, we only need to calculate the area of one triangle.
Area of a triangle = 1/2 * base * height
Area of one triangle = 1/2 * 3 inches * 4 inches = 6 square inches
Area of both triangles = 2 * 6 square inches = 12 square inches
2. Total area of the composite shape:
Given that the total area of the composite shape is 40 square inches and the area of the triangles is 12 square inches, the area of the rectangle can be found by subtracting the area of the triangles from the total area.
Area of the rectangle = 40 square inches - 12 square inches = 28 square inches
Therefore, the area of the rectangle within the composite shape is 28 square inches.