Answer:
96 ft²
Step-by-step explanation:
The general formula for the surface area of a pyramid is:
SA = [tex]\frac{1}{2}[/tex]pl + B, were p = the perimeter of the base, l = the slant height and B = the area of the base
Since the area of the base is 36 ft², then each side is √36, or 6 ft. The perimeter is the sum of all the sides, so 6 x 4 = 24 ft.
Given the overall height of the pyramid is 4 feet, you can use the Pythagorean Theorem (a² + b² = c²) to find the slant height (hypotenuse) of the pyramid. Using 3 feet for 'a' and 4 feet for 'b':
3² + 4² = c² or 9 + 16 = 25
25 = c² or c = 5
SA = [tex]\frac{1}{2}[/tex](24)(5) + 36
SA = 60 + 36 = 96 ft²
