Sure, let's find the volume of a pyramid with a square base given the perimeter of the base and the height of the pyramid.
1. Determine the side length of the square base:
- The perimeter of a square is the sum of all four sides.
- Given perimeter: [tex]\( 8.7 \text{ ft} \)[/tex]
- To find the length of one side, divide the perimeter by 4:
[tex]\[
\text{Side length} = \frac{\text{Perimeter}}{4} = \frac{8.7 \text{ ft}}{4} = 2.175 \text{ ft}
\][/tex]
2. Calculate the area of the square base:
- The area of a square is found by squaring the side length:
[tex]\[
\text{Base Area} = (\text{Side length})^2 = (2.175 \text{ ft})^2 = 4.730625 \text{ ft}^2
\][/tex]
3. Determine the volume of the pyramid:
- The volume of a pyramid is given by the formula:
[tex]\[
\text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\][/tex]
- Given height: [tex]\( 9.2 \text{ ft} \)[/tex]
- Substitute the values into the formula:
[tex]\[
\text{Volume} = \frac{1}{3} \times 4.730625 \text{ ft}^2 \times 9.2 \text{ ft} = 14.50725 \text{ ft}^3
\][/tex]
4. Round the volume to the nearest tenth:
- The volume, [tex]\( 14.50725 \text{ ft}^3 \)[/tex], rounded to the nearest tenth is:
[tex]\[
14.5 \text{ ft}^3
\][/tex]
Therefore, the volume of the pyramid is [tex]\( 14.5 \text{ ft}^3 \)[/tex].
