Question

The pyramid of teti has a square base with edge length of 202.5 yds. and a slant height of 175.1 yds find the height of the pyramid round to the nearest tenth

Answer 1

To find the height of the pyramid, we can use the Pythagorean theorem. The pyramid has a square base, which means the height, the slant height, and half the base edge length form a right triangle.

1. **Determine half the length of the base edge**:
\[
\text{Half base edge} = \frac{\text{Edge length}}{2} = \frac{202.5 \text{ yds}}{2} = 101.25 \text{ yds}
\]

2. **Set up the Pythagorean theorem**:
\[
\text{slant height}^2 = \text{height}^2 + \left(\text{Half base edge}\right)^2
\]
Let \( h \) be the height of the pyramid:
\[
175.1^2 = h^2 + 101.25^2
\]

3. **Calculate \( 175.1^2 \) and \( 101.25^2 \)**:
\[
175.1^2 = 30645.01
\]
\[
101.25^2 = 10253.0625
\]

4. **Substituting into the equation**:
\[
30645.01 = h^2 + 10253.0625
\]

5. **Solving for \( h^2 \)**:
\[
h^2 = 30645.01 - 10253.0625
\]
\[
h^2 = 20391.9475
\]

6. **Taking the square root to find \( h \)**:
\[
h = \sqrt{20391.9475} \approx 142.0 \text{ yds}
\]

Therefore, the height of the pyramid rounded to the nearest tenth is **142.0 yards**.