The net of a right pyramid with a square base is shown. The surface area is 90 square inches. The side of the square base is 6 inches. What is the area, in square inches, of each triangular face?

Rationale

The area of each triangular face is 13.5 square inches.

To find the area of each triangular face of the right pyramid, we first determine the height of the triangular face using the formula for the surface area of the pyramid and then calculate the area of the triangle.

A (13.5) CORRECT

This is the correct answer. The area of each triangular face is calculated by first finding the height of the triangles. The total area of the four triangular faces must equal the remaining surface area after subtracting the area of the base from the total surface area. The area of the base is 36 square inches (6 inches × 6 inches), leaving 54 square inches for the triangular faces. Dividing this by 4 gives 13.5 square inches for each triangular face.

B (18) YOUR ANSWER

An area of 18 square inches for each triangular face would imply that the total area of the four triangular faces sums to 72 square inches. This is incorrect because when added to the area of the square base (36 square inches), the total would exceed the given surface area of 90 square inches.

C (22.5) YOUR ANSWER

If each triangular face had an area of 22.5 square inches, the total area for four triangular faces would be 90 square inches. This would leave no area for the square base, which contradicts the given surface area of 90 square inches that includes both the base and the triangular faces.

D (54) YOUR ANSWER

An area of 54 square inches for each triangular face would mean that the total area of the four triangular faces is 216 square inches. This clearly exceeds the total surface area of 90 square inches, indicating a misunderstanding of the relationship between the triangular faces and the base area.

Conclusion

The area of each triangular face of the right pyramid is determined by the remaining surface area after accounting for the base. With a pyramid surface area of 90 square inches and a base area of 36 square inches, the correct area of each triangular face is calculated to be 13.5 square inches. Other options do not align with the constraints given in the problem and thus cannot be correct.

The net of a right pyramid with a square base is shown. The surface area is 90 square inches. The side of the square base is 6 inches. What is the area, in square inches, of each triangular face?

The area of each triangular face is 13.5 square inches.

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