Fatima measures this square-based pyramid. She finds that its volume is 52 cubic feet. What is the height of Fatima’s pyramid? A = 13 ft.^2 (1 point) Responses 4 ft. 4 ft. 12 ft. 12 ft. 225 ft. 225 ft. 10 ft. 10 ft.

Answer 1

To find the height of the square-based pyramid, we can use the formula for the volume of a pyramid:

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

Where:

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

In this case, we know:

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

We can rearrange the formula to solve for the height (\(h\)):

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

Now, plug in the values for \(V\) and \(A\):

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

Calculating this gives:

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

Therefore, the height of Fatima's pyramid is \(12\) feet.