To find the length of each side of the base of the pyramid, we need to use the formula for the volume of a pyramid, which is:
\(\[ \text{Volume} = \frac{1}{3} \times \text{base area} \times \text{height} \]\)
Given:
- Volume (\(\( V \)\)) = 132 cubic centimeters
- Height (\(\( h \)\)) = 11 centimeters
- The base of the pyramid is a square, so if \(\( s \)\) is the side length of the square base, the base area would be \(\( s^2 \)\).
We start by isolating the base area in the volume formula:
\(\[ 132 = \frac{1}{3} \times s^2 \times 11 \]\)
First, multiply both sides of the equation by 3 to eliminate the fraction:
\(\[ 396 = s^2 \times 11 \]\)
Next, divide both sides by 11 to solve for \(\( s^2 \)\):
\(\[ \frac{396}{11} = s^2 \]\)
\(\[ s^2 = 36 \]\)
To find \(\( s \)\), take the square root of both sides:
\(\[ s = \sqrt{36} \]\)
\(\[ s = 6 \]\)
So, the length of each side of the base of the pyramid is \(\( \boxed{6} \)\) centimeters.
