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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

10 ft.
10 ft.

12 ft.
12 ft.

4 ft.
4 ft.

225 ft.
225 ft.

Answer 1

To find the height of Fatima's triangular pyramid with a square base, we can use the formula for the volume of a pyramid:

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

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

From the problem, we know:

• \( V = 52 \) cubic feet
• \( B = a = 13 \) square feet

Now, we can plug these values into the volume formula:

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

To solve for \( h \), first multiply both sides by 3:

\[ 156 = 13 \cdot h \]

Next, divide both sides by 13:

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

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