Question

Use the image to answer the 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.

10 ft.
10 ft.

12 ft.
12 ft.

225 ft.
225 ft.
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Answer 1

To find the height of Fatima’s pyramid, we can use the formula for the volume of a pyramid:

\[
V = \frac{1}{3} \times B \times h
\]

where \( V \) is the volume, \( B \) is the area of the base, and \( h \) is the height.

From the information provided:
- Volume, \( V = 52 \) cubic feet
- Area of the base, \( B = 13 \) square feet

We can substitute these values into the formula:

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

To solve for \( h \), we first isolate \( h \):

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

Multiplying both sides by 3 to eliminate the fraction:

\[
156 = 13h
\]

Now, divide both sides by 13:

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

Thus, the height of Fatima’s pyramid is \( \boxed{12} \) feet.