Question

a camping tent is in the shape of a square pyramid. the sides of the tent are 15 yards and the edge length is 18 yards. find the height of the pyramid. round the answer to the nearest tenth. the height of the pyramid is yards. check answer remaining attempts : 2 view previous attempt

Explanation:

Step1: Find the distance from the center of the base to a vertex

Since the base is a square with side length \(s = 15\) yards. The distance \(d\) from the center of the square base to a vertex is given by \(d=\frac{\sqrt{2}}{2}s\).
Substitute \(s = 15\) into the formula: \(d=\frac{\sqrt{2}}{2}\times15=\frac{15\sqrt{2}}{2}\approx10.6\) yards.

Step2: Use the Pythagorean theorem

Let the edge length of the pyramid be \(l = 18\) yards and the height of the pyramid be \(h\). According to the Pythagorean theorem \(l^{2}=h^{2}+d^{2}\).
We can solve for \(h\): \(h=\sqrt{l^{2}-d^{2}}\).
Substitute \(l = 18\) and \(d\approx10.6\) into the formula: \(h=\sqrt{18^{2}-( \frac{15\sqrt{2}}{2})^{2}}=\sqrt{324 - \frac{225\times2}{4}}=\sqrt{324 - 112.5}=\sqrt{211.5}\approx14.5\) yards.

Answer:

\(14.5\)