Question

a circus tent is the shape of a square pyramid it has a base edge of 20meter, a slant height of 13.5 find the height of the tent round to earth tenth

Answer 1

To find the height of the circus tent, which is shaped like a square pyramid, we can use the Pythagorean theorem. In a square pyramid, the height, the slant height, and half of the base edge form a right triangle.

1. **Identify the dimensions**:
- Base edge (side length of the square base) = 20 meters
- Half of the base edge = \( \frac{20}{2} = 10 \) meters
- Slant height = 13.5 meters

2. **Set up the Pythagorean theorem**:
Let \( h \) be the height of the pyramid. According to the Pythagorean theorem:
\[
\text{slant height}^2 = \text{height}^2 + \left(\frac{\text{base edge}}{2}\right)^2
\]
Substituting the values we have:
\[
13.5^2 = h^2 + 10^2
\]

3. **Calculate \( 13.5^2 \) and \( 10^2 \)**:
\[
13.5^2 = 182.25
\]
\[
10^2 = 100
\]

4. **Plug these values into the equation**:
\[
182.25 = h^2 + 100
\]

5. **Solve for \( h^2 \)**:
\[
h^2 = 182.25 - 100 = 82.25
\]

6. **Find \( h \)**:
\[
h = \sqrt{82.25} \approx 9.065
\]

7. **Round to the nearest tenth**:
\[
h \approx 9.1 \text{ meters}
\]

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