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: Calculate base area

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

Step2: Calculate area of one triangular face

The formula for the area of a triangle is $A=\frac{1}{2}bh$, where the base $b$ of each triangular face is the side - length of the base of the pyramid ($b = 339$ feet) and the height of each triangular face is the slant height $l = 274$ feet. So, the area of one triangular face $A_{1}=\frac{1}{2}\times339\times274 = 46587$ square feet.

Step3: Calculate total area of 4 triangular faces

Since a square pyramid has 4 triangular faces, the total area of the 4 triangular faces $A_{triangles}=4\times A_{1}=4\times46587 = 186348$ square feet.

Step4: Calculate total surface area to be inspected

The total surface area $S$ to be inspected is the sum of the base area and the area of the 4 triangular faces. So, $S = B+A_{triangles}=114921 + 186348=301269$ square feet.

Answer:

301269