A triangular pyramid has a surface area of 336 square inches. It is made up of equilateral triangles with side lengths of 12 inches. What is the slant height?

Given:

Surface Area = 336 sq. inches

side lengths = 12 inches

equilateral triangles

find the slant height.

Area of an equilateral triangle = √3/4 * a² = √3/4 * (12in) = 62.35 in²

Perimeter = 3 a = 3 * 12 = 36 inches

Surface Area = Base Area + 1/2 Perimeter * Slant height

336 in² = 62.35 in² + 1/2 * 36 in * slant height

336 in² - 62.35 in² = 1/2 * 36 in * slant height

273.65 in² * 2 = 36 in * slant height

547.30 in² = 36 in * slant height

547.30 in² / 36 in = slant height

15.20 in = slant height.