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
7 square inches
7 square inches
16 square inches
16 square inches
34 square inches
34 square inches
28 square inches
28 square inches
To find the area of the rectangle within the composite shape, we need to find the area of the entire composite shape and then subtract the areas of the two congruent right triangles.
The area of the composite shape is given as 40 square inches.
The area of one right triangle is (1/2) * base * height = (1/2) * 3 * 4 = 6 square inches.
Since there are two congruent right triangles, the total area of the two triangles would be 2 * 6 = 12 square inches.
To find the area of the rectangle within the composite shape, we can subtract the total area of the triangles from the area of the composite shape.
Area of rectangle = Area of composite shape - Area of triangles
Area of rectangle = 40 square inches - 12 square inches = 28 square inches.
Therefore, the area of the rectangle within the composite shape is 28 square inches.