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