Question

A circus tent is in the shape of a square pyramid each edge of the square is 20 m and its slant height is 13.5 find the height of the tent

Answer 1

To find the height of the square pyramid (circus tent), we can use the Pythagorean theorem.

Given:
- The length of each edge of the square base is \( a = 20 \) m.
- The slant height \( l = 13.5 \) m.

First, we need to find the height \( h \) of the pyramid. The slant height is the distance from the apex (top) of the pyramid down to the midpoint of one of the edges of the base square. Hence, the relationship we can use is:

\[
l^2 = h^2 + \left(\frac{a}{2}\right)^2
\]

Where \( \frac{a}{2} \) is half the length of the base, which represents the horizontal distance from the apex to the midpoint of one side of the base.

1. Calculate \( \frac{a}{2} \):
\[
\frac{a}{2} = \frac{20}{2} = 10 \text{ m}
\]

2. Substitute \( l \) and \( \frac{a}{2} \) into the equation:
\[
(13.5)^2 = h^2 + (10)^2
\]

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

4. Rearranging gives:
\[
h^2 = 182.25 - 100 = 82.25
\]

5. Finally, take the square root to find \( h \):
\[
h = \sqrt{82.25} \approx 9.06 \text{ m}
\]

Thus, the height of the circus tent is approximately \( 9.06 \) meters.