The Pyramid of Khafre in Egypt stands 471 feet tall. The sides of its square base are 705 feet in length. Find the lateral surface area of the Pyramid of Khafre. (Hint: Use the Pythagorean Theorem to find the pyramid's slant height)

Lateral surface area = 4 (1/2 * 705 * 588.30) = 829503 ft²

Step-by-step explanation:

The pyramid is a square base pyramid. The height = 471 ft. The sides of the square base pyramid = 705 ft.

To calculate the lateral area of the square base pyramid we have to know the slant height. The slant height can be known by using Pythagoras theorem to solve for it.

c² = a² + b² (Pythagoras theorem)

base = b = 705/2 = 352.50 ft

c² = 352.50² + 471²

c² = 124256.25 + 221841

c² = 346097.25

square root both sides

c = √346097.25

c = 588.300305966

c ≈ 588.30 ft

slant height = 588.30 ft

Lateral surface area = sum of area of the 4 triangular faces

lateral surface area = 4 (1/2 * base * height)

Lateral surface area = 4 (1/2 * 705 * 588.30) = 829503 ft²