The base area of a regular quadrangular prism is 169 cm ^ 2 and the height is 10 cm

The base area of a regular quadrangular prism is 169 cm ^ 2 and the height is 10 cm, find the areas of the side and full surfaces of this prism.

Since the prism is correct, then there are squares at the base, from the area of the square we should find the length of its side:
S = a ^ 2 => a = (S) ^ (1/2).
a = 13 cm.
The length of the side of the square is 13 cm, then we find the perimeter of the base:
P = 4а = 4 * 13 = 52 cm.
Let us find the area of the lateral surface of the prism:
Sb = P * l, where l is the height of the prism.
Sb = 52 * 10 = 520 cm2.
Find the total surface area of the prism:
Sp = Sb + 2Sb = 520 + 2 * 169 = 858 cm2.
Answer: 520 cm2 and 858 cm2