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Question

A triangular pyramid with a square base has a dotted line segment labeled h equals question mark extending from the top vertex to the base. The base of the pyramid is labeled a equals 13 feet squared.

Fatima measures this square-based pyramid. She finds that its volume is 52 cubic feet. What is the height of Fatima’s pyramid?

(1 point)
Responses

4 ft.
4 ft.

12 ft.
12 ft.

225 ft.
225 ft.

10 ft.

Answer 1

The formula for the volume \( V \) of a triangular pyramid (or any pyramid) is given by:

\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

In this case, the base area \( A \) is given as 13 square feet and the volume \( V \) is 52 cubic feet. We can plug these values into the formula to solve for the height \( h \).

\[ 52 = \frac{1}{3} \times 13 \times h \]

To isolate \( h \), we first multiply both sides by 3:

\[ 156 = 13 \times h \]

Next, divide both sides by 13:

\[ h = \frac{156}{13} = 12 \]

Thus, the height of Fatima’s pyramid is 12 ft.