Question

The Great Pyramid of Giza is an example of a square pyramid and is the last surviving structure considered a wonder of the ancient world. The builders of the pyramid used a measure called a cubit, which represents the length of the forearm from the elbow to the tip of the middle finger. One cubit is about 20 inches in length.

One side of the base is measured to be 453 cubits and the lateral surface area is 260,928 squared cubits.

What is the height (in cubits) of the pyramid?

What is the total surface area (in squares cubits) of the pyramid?

Answer 1

a) 177.9 cubits

b) 466137 squared cubits

Explanation:

Given that:

The length of the base (b) = 453 cubits, lateral surface area (a) = 260928, the height of the pyramid (h)

a)

The formula of the lateral surface area is given as:

`a=b√(b^2+4h^2)`

Therefore:

`260928=453√(453^2+4h^2)\\576=√(453^2+4h^2)\\576^2=453^2+4h^2\\4h^2=576^2-453^2=126567\\h^2=31641.75\\h=√(31641.75)\\ h=177.9`

h = 177.9 cubits

b) total surface area = area of base + lateral surface area = b² + lateral surface area

total surface area = 453² + 260928 = 466137 squared cubits