Question

The composite shape in the image has an area of 40 square inches. What is the area of the rectangle within the composite shape?
the triangle 3in lenght 4in height 2 triangle base is 3in
(1 point)
Responses

34 square inches
34 square inches

28 square inches
28 square inches

16 square inches
16 square inches

7 square inches

Answer 1

To determine the area of the rectangle within the composite shape, we first need to calculate the total area occupied by the triangles.

You mentioned that there are two triangles, each with a base of 3 inches and a height of 4 inches. The area \(A\) of a triangle can be calculated using the formula:

\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]

For one triangle:

\[
A_{\text{triangle}} = \frac{1}{2} \times 3 \, \text{in} \times 4 \, \text{in} = \frac{1}{2} \times 12 \, \text{in}^2 = 6 \, \text{in}^2
\]

Since there are two triangles:

\[
A_{\text{two triangles}} = 2 \times 6 \, \text{in}^2 = 12 \, \text{in}^2
\]

The total area of the composite shape is given as 40 square inches. To find the area of the rectangle, we subtract the area of the triangles from the total area:

\[
A_{\text{rectangle}} = \text{Total Area} - A_{\text{two triangles}} = 40 \, \text{in}^2 - 12 \, \text{in}^2 = 28 \, \text{in}^2
\]

Therefore, the area of the rectangle within the composite shape is **28 square inches**.