Question

The Great pyramid of Giza has a square base with side length 755 ft. and original height of 481 ft. Determine its surface area. The answer is 923,285 ft. But i don't know how to get that answer. Please help.

Answer 1

The surface of pyramid is calculated by summing surface of its base and surface of its mantle.

Surface of base is easy to calculate. You have a square and its side is known therefore surface is:
Sb = a^2
Surface of mantle is a bit more complicated to calculate. First you have 4 sides of pyramid and each side is a triangle. To calculate surface of each triangle we need to know its height.
First we calculate side of triangle using Pitagorah's theorem.
s = √((d/2)^2 + H^2) where d is diagonal of base which is square.
d = √2*a

Now again we have to use Pitagorah's theorem to calculate height of the triangle.
h = √(s^2 - (a/2)^2)

Now the surface of the triangle is calculated with:
St = (a*h)/2 and surface of mentle is:
Sm = 4*St.

Total surface of pyramid is:
Sb + Sm