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 $b$ is the base and $h$ is the height. For the triangular faces of the square - pyramid, $b = 339$ feet (base of the triangle, which is the side - length of the square base) and $h = 274$ feet (slant height). So the area of one triangular face $A_{1}=\frac{1}{2}\times339\times274 = 46587$ square feet.

Step3: Calculate total area of four triangular faces

Since there are 4 triangular faces, the total area of the triangular faces $A_{t}=4\times A_{1}=4\times46587 = 186348$ square feet.

Step4: Calculate total surface area to be inspected

The total surface area $S$ of the square - pyramid (the area the architect needs to inspect) is the sum of the base area and the total area of the triangular faces. So $S=B + A_{t}=114921+186348=301269$ square feet.

Answer:

301269