Find the side of the base and the height of a regular four-angle prism if its total surface is 228 cm2

Find the side of the base and the height of a regular four-angle prism if its total surface is 228 cm2 and the side surface is 100 cm2

If we subtract the side surface Sb from the total surface of the prisms S, then the difference will be equal to the area of the two bases:

S – Sb = 2Sо

Find the base area:

2Sо = (S – Sb) / 2 = (228 cm ^ 2 – 100 cm ^ 2) / 2 = 64 cm ^ 2.

The base side a is found as the side of the square with area So:

a = √Sо = √ (64 cm ^ 2) = 8 cm.

The perimeter of the base is equal to the perimeter of the square:

p = 4a = 4 * 8 cm = 32 cm.

The side area Sb is equal to the product of the perimeter p by the height of the prism h:

Sb = ph;

h = Sb / p = (100 cm ^ 2) / (32 cm) = 25/8 cm = 3.125 cm.

Answer. Side a = 8 cm, height h = 3.125 cm.