Question

a circus tent is the shape of a square pyramid it has a base endge of 20 meters a slant height of 13.5 m find the height and round to the nearest tenths

Answer 1

To find the height of a square pyramid (circus tent), we can use the relationship between the slant height, height, and half the base edge.

Given:
- Base edge \( a = 20 \) meters
- Slant height \( l = 13.5 \) meters

First, we need to find half the base edge, which is:

\[
\frac{a}{2} = \frac{20}{2} = 10 \text{ meters}
\]

Now, we can use the Pythagorean theorem, which relates the height \( h \), half the base edge, and the slant height:

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

Substituting the values we have:

\[
(13.5)^2 = h^2 + (10)^2
\]

Calculating the squares:

\[
182.25 = h^2 + 100
\]

Now, subtract 100 from both sides:

\[
182.25 - 100 = h^2
\]

\[
82.25 = h^2
\]

Now, take the square root of both sides to find \( h \):

\[
h = \sqrt{82.25} \approx 9.1 \text{ meters}
\]

Thus, the height of the circus tent, rounded to the nearest tenth, is approximately **9.1 meters**.