Answer: She will need 1239 cm^3 of foil
Explanation:
Surface area of square pyramid = base area of square + area of 4 triangular faces
Area of square base = l^2
where
l is the length of each side of the square base
From the information given,
l = 8
Area of square base = 8^2 = 64
Area of each triangular face = 1/2 x base x height
We would find the height of each face by applying Pythagorean theorem to the right triangle formed below. It is ex[ressed as
hypotenuse^2 = one leg^2 + other leg^2
hypotenuse = 10
one leg = 4
other leg = h
4^2 + h^2 = 10^2
36 + h^2 = 100
h^2 = 100 - 36 = 64
h = √64
h = 8
base = 8
Area of 4 triangular faces 4 x 1/2 x 8 x 8 = 128
Surface area of square base pyramid = 128 + 64 = 192 in^2
We would convert 192 in^2 cm^2
Recall,
1 inch^2 = 6,4516 cm^2
192 inch^2 = 192 x 6.4516
= 1239 cm^2
She will need 1239 cm^3 of foil
