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 lenght 3in the base 3in the hight 4in
(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 can use the information given about the rectangle's dimensions.

The dimensions of the rectangle are as follows:
- Length = 3 inches
- Height = 4 inches

The area of the rectangle can be calculated using the formula:
\[
\text{Area} = \text{Length} \times \text{Height}
\]

Substituting the given dimensions:
\[
\text{Area} = 3 \, \text{inches} \times 4 \, \text{inches} = 12 \, \text{square inches}
\]

Now that we have the area of the rectangle, we examine this relative to the total area of the composite shape which is 40 square inches.

If the area of the rectangle is 12 square inches, we can find the area outside the rectangle in the composite shape:
\[
\text{Area outside the rectangle} = \text{Total Area} - \text{Area of Rectangle}
\]
\[
\text{Area outside the rectangle} = 40 \, \text{square inches} - 12 \, \text{square inches} = 28 \, \text{square inches}
\]

The area of the rectangle within the composite shape, however, is 12 square inches.

Looking closely at your responses:
- 34 square inches
- 28 square inches
- 16 square inches
- 7 square inches

None of these match the calculated area of the rectangle which is 12 square inches.

If this was possibly an error in provided dimensions or calculations, could you clarify any changes or additional data? Otherwise, based purely on the information initially provided, the area of the rectangle is 12 square inches.