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 to the nearest tenth.
The height of the tent can be found by using the Pythagorean theorem.
Let's call the height of the tent h. Then, we can create a right triangle with one leg being half of the length of an edge of the square base (10 m) and the other leg being the height of the tent (h). The slant height of the pyramid is the hypotenuse.
Using the Pythagorean theorem, we have:
\[h^2 + 10^2 = 13.5^2\]
\[h^2 + 100 = 182.25\]
\[h^2 = 82.25\]
\[h = \sqrt{82.25}\]
\[h \approx 9.1\]
The height of the tent is approximately 9.1 m.