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 sed 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 cihits and the lateral surface area is 260,928 squared cubits.

what is the surface area ( 100 Points)

Answer 1

The surface area of the pyramid is 335,673 cubit² or 134,269,200 in.²

Explanation:

Here we have that the formula for the lateral surface area of a square pyramid is given as follows;

Lateral surface area = 2 × b × h

Where:

b = Base length = 453 cubits

h = Slant height

∴ 260,928 = 2 × 453 × h

Hence;

h = (260,928)/(2 × 453) = 288 cubits

We therefore have

Length of side, s = 453 cubits = 453*20 inches = 9060 in.

Slant height = 288*20 inches = 3300 in.

Surface area of the pyramid = A + 1/2 × p × s

Where:

A = Area of the base = s² = 453² = 205209 cubit²

p = Perimeter of base = 2×s = 2×453 = 906 cubit

s = Slant height = 288 cubit

∴ Surface area of the pyramid = 205209 + 1/2 × 906× 288

Surface area of the pyramid = 335,673 cubit²

1 cubit = 20 in

∴ 1 cubit² = 400 in²

335,673 cubit² = 400×335,673 = 134,269,200 in.² ‪= 932,425 ft²