Question

the great pyramid of giza in egypt has a square base with edge length of 230.5 m and a slant height of 180.2 m. find the height of the pyramid. round the answer to the nearest tenth. (1 point)

Explanation:

Step1: Calculate half of the base edge length

The base is a square with edge length \(a = 230.5\) m. Half of the base edge length \(s=\frac{230.5}{2}=115.25\) m.

Step2: Use the Pythagorean theorem

Let the height of the pyramid be \(h\), the slant height \(l = 180.2\) m. According to the Pythagorean theorem \(h=\sqrt{l^{2}-s^{2}}\).
Substitute \(l = 180.2\) and \(s=115.25\) into the formula:
\(h=\sqrt{180.2^{2}-115.25^{2}}=\sqrt{(180.2 + 115.25)(180.2-115.25)}\) (using \(a^{2}-b^{2}=(a + b)(a - b)\))
\(=\sqrt{(295.45)(64.95)}\)
\(=\sqrt{19199.47}\approx138.6\)

Answer:

\(138.6\)