The composite shape in the image has an area of 40 square inches. What is the area of the rectangle within the composite shape?

Question

(1 point)
Responses

7 square inches
7 square inches

34 square inches
34 square inches

16 square inches
16 square inches

28 square inches

The image shows a triangle on the left of the rectangle. That triangle’s base is 3 inches. The rectangle is in the middle. The hight of it is 4 inches. The base is unknown. On the right there is another triangle. That triangles base is 3 inches and the hight is 4 inches.

Answer 1

To find the area of the rectangle within the composite shape, we can start by calculating the areas of the triangles and then use the total area of the composite shape to find the area of the rectangle.

1. Calculating the area of the left triangle:

   • Base = 3 inches
   • Height = 4 inches
   • Area = (1/2) * base * height = (1/2) * 3 * 4 = 6 square inches

2. Calculating the area of the right triangle:

   • Base = 3 inches
   • Height = 4 inches
   • Area = (1/2) * base * height = (1/2) * 3 * 4 = 6 square inches

3. Calculating the total area of both triangles:

   • Total area of triangles = Area of left triangle + Area of right triangle = 6 + 6 = 12 square inches

4. Finding the area of the rectangle:

   • Total area of the composite shape = 40 square inches
   • Area of the rectangle = Total area - Total area of triangles = 40 - 12 = 28 square inches

So, the area of the rectangle is 28 square inches.