Find the Lateral AND Total Surface Area of a pyramid with slant height 6.8mi whose triangular base measures 11mi on each side. Each altitude of the base measures 9.5mi.

Step-by-step explanation:

The given pyramid is a square based pyramid. The formula for determining the lateral surface area of a square base pyramid is expressed as

Lateral surface area = 1/2 * perimeter * slant height

From the information given,

Length of each side = 11 miles

Perimeter of base = 4 * 11 = 44 miles

Slant height = 6.8 miles

Lateral surface area = 1/2 * 44 * 6.8 = 149.6 miles²

The formula for determining the total surface area of a square base pyramid is expressed as

Total surface area = base area + (1/2 * perimeter * slant height)

Base area = 11² = 121

Total surface area = 121 + (1/2 * 44 * 6.8) = 270.6 miles²