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.

Question

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.

10 ft.
10 ft.

225 ft.

Answer 1

To find the height (h) of a square-based pyramid given its volume (V) and the area of the base (A), you can use the formula for the volume of a pyramid:

\[ V = \frac{1}{3} A h \]

Where:

• \( V \) is the volume of the pyramid,
• \( A \) is the area of the base,
• \( h \) is the height.

Given:

• \( V = 52 \) cubic feet
• \( A = 13 \) square feet

Now, we can plug these values into the formula and solve for \( h \):

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

To eliminate the fraction, multiply both sides by 3:

\[ 3 \times 52 = 13h \]

\[ 156 = 13h \]

Now, divide both sides by 13 to solve for \( h \):

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

\[ h = 12 \text{ feet} \]

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