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 : 3
question 3
bruce wants to ship a fishing pole to his brother. the longest cylinder - shaped container available for shipping has a diameter of 13 in. and a height of 84 in. what is the longest fishing pole bruce can ship to his brother?

Explanation:

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

The base is a square with side length \(s = 15\) yards. The distance from the center of a square to a vertex \(d=\frac{\sqrt{2}}{2}s\).
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 know \(l = 18\) and \(d\approx10.6\), so we can solve for \(h\):

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Answer:

\(9.9\)