Question

the pyramid of menkaure is a square pyramid located in giza. the pyramid has a height of about 215 feet, a slant height of about 274 feet, and a base side length of about 339 feet. after a windstorm, an architect was tasked with inspecting the outer surfaces of the pyramid for damage. how many square feet does the architect need to inspect? type the correct answer in the box. use numerals instead of words. the architect will need to inspect square feet.

Explanation:

Step1: Find area of base

The base is a square with side length $s = 339$ feet. The area of the base $A_{base}=s^{2}$. So $A_{base}=339^{2}=114921$ square - feet.

Step2: Find area of one triangular face

The formula for the area of a triangle is $A=\frac{1}{2}bh$, where the base $b$ is the side - length of the square base and the height $h$ is the slant height. Here, $b = 339$ feet and $h = 274$ feet. So the area of one triangular face $A_{triangle}=\frac{1}{2}\times339\times274 = 46542$ square feet.

Step3: Find area of four triangular faces

Since there are 4 triangular faces on a square pyramid, the total area of the triangular faces $A_{triangles}=4\times A_{triangle}=4\times46542 = 186168$ square feet.

Step4: Find total surface area to inspect

The total surface area $A$ that the architect needs to inspect is the sum of the area of the base and the area of the four triangular faces. So $A=A_{base}+A_{triangles}=114921 + 186168=301089$ square feet.

Answer:

301089