The composite shape in the image has an area of 40 square inches. What is the area of the rectangle within the composite shape?
To find the area of the rectangle within the composite shape, we need to subtract the area of the three triangles from the total area of the composite shape.
The total area is given as 40 square inches. The composite shape consists of three triangles and a rectangle. Let's denote the area of the rectangle as x square inches.
The area of the three triangles is given by (1/2)bh, where b represents the base and h represents the height of each triangle. Since the height and base of each triangle are the same as the sides of the rectangle, the area of each triangle is (1/2)(3)(2) = 3 square inches.
Since there are three triangles, the total area of the triangles is 3 + 3 + 3 = 9 square inches.
Now, to find the area of the rectangle, we can subtract the total area of the triangles from the total area of the composite shape:
Total area - Total area of triangles = Area of rectangle
40 - 9 = x
31 = x
Therefore, the area of the rectangle within the composite shape is 31 square inches.