Question

A circus tent is in the shape of a square pyramid. Each edge of the square base is 20 m and its slant height is 13.5 m. Find the height of the tent. Round the answer to the nearest tenth. (1 point) 16.8 m 14.8 cm 9.1m 24.1 cm

Answer 1

To find the height of the square pyramid (circus tent), we can use the Pythagorean theorem. The slant height (l) of the pyramid forms a right triangle with the height (h) of the pyramid and half the length of the base (b/2).

1. **Find the half-base length**:
The length of each edge of the square base is 20 m, so:
\[
b = 20 \text{ m}
\]
Half of the base length is:
\[
\frac{b}{2} = \frac{20}{2} = 10 \text{ m}
\]

2. **Use the Pythagorean theorem**:
The relationship between the height (h), the slant height (l), and half the base length is given by:
\[
l^2 = h^2 + \left(\frac{b}{2}\right)^2
\]
Plugging in the values:
\[
13.5^2 = h^2 + 10^2
\]

3. **Calculate**:
\[
182.25 = h^2 + 100
\]
\[
h^2 = 182.25 - 100 = 82.25
\]
\[
h = \sqrt{82.25} \approx 9.1 \text{ m}
\]

Thus, the height of the tent is approximately **9.1 m**.