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

28 square inches
28 square inches

7 square inches
7 square inches

34 square inches
34 square inches

16 square inches

1 answer

To find the area of the rectangle within the composite shape, we first need to calculate the area of the two congruent right triangles.

The area of one right triangle can be calculated using the formula: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] Given that the base (width) of each triangle is 3 inches and the height is 4 inches, we can calculate the area of one triangle:

\[ \text{Area of one triangle} = \frac{1}{2} \times 3 \times 4 = \frac{1}{2} \times 12 = 6 \text{ square inches} \]

Since there are two congruent triangles, the total area of the triangles is:

\[ \text{Total area of triangles} = 2 \times 6 = 12 \text{ square inches} \]

Now, we know the total area of the composite shape, which is 40 square inches. To find the area of the rectangle, we can subtract the total area of the triangles from the total area of the composite shape:

\[ \text{Area of rectangle} = \text{Total area of composite shape} - \text{Total area of triangles} \] \[ \text{Area of rectangle} = 40 - 12 = 28 \text{ square inches} \]

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

Therefore, the correct response is: 28 square inches.