Question

find the slant height of this square pyramid.

Explanation:

Step1: Analyze the right - triangle

The base of the right - triangle (half of the side length of the square base) is \(a = \frac{6}{2}=3\) inches, and the hypotenuse (the edge of the pyramid) is \(c = 6\) inches. Let the slant height be \(l\).

Step2: Apply the Pythagorean theorem

By the Pythagorean theorem \(l=\sqrt{c^{2}-a^{2}}\). Substitute \(a = 3\) and \(c = 6\) into the formula: \(l=\sqrt{6^{2}-3^{2}}=\sqrt{36 - 9}=\sqrt{27}=3\sqrt{3}\approx3\times1.732 = 5.196\) inches.

Answer:

The slant height of the square pyramid is \(3\sqrt{3}\approx5.2\) inches.