Question

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?

Answer 1

It is actually fourteen...you didvide 336 by 12 and since that slant is a triangle based shape you divide that by the quotient of 336\12, which is 14. Sorry if it’s a little confusing

Answer 2

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.