Question

the pyramid of merikaure 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: Calculate area of base

The base is a square. Area of square $A_{base}=s^2$, where $s = 339$ feet. So $A_{base}=339^2= 114921$ square - feet.

Step2: Calculate area of one triangular face

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

Step3: Calculate total area of 4 triangular faces

Since there are 4 triangular faces, $A_{triangles}=4\times A_{\triangle}=4\times46542 = 186168$ square - feet.

Step4: Calculate total surface area to be inspected

The total surface area $A = A_{base}+A_{triangles}=114921 + 186168=301089$ square - feet.

Answer:

301089