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) 14.8 cm 26.8 m 24.1 cm 9.1 m

Explanation:

Step1: Find half of the base edge

The base is a square with edge length \(20\) m. Half of the base edge \(a=\frac{20}{2} = 10\) m.

Step2: Apply the Pythagorean theorem

Let the height of the pyramid be \(h\), the slant height \(l = 13.5\) m. By the Pythagorean theorem \(h=\sqrt{l^{2}-a^{2}}\).
Substitute \(l = 13.5\) and \(a = 10\) into the formula: \(h=\sqrt{13.5^{2}-10^{2}}=\sqrt{182.25 - 100}=\sqrt{82.25}\approx9.1\) m.

Answer:

\(9.1\) m (the fourth option)