ABCDA1B1C1D1 is the correct prism. Its total surface area is 210 m2, and the side surface area is 160 m2.

ABCDA1B1C1D1 is the correct prism. Its total surface area is 210 m2, and the side surface area is 160 m2. Find the side of the base and the height of the prism.

Since the pyramid is regular and quadrangular, there is a square at its base.

Find the area of the base of the prism.

Sb = S floor – S side = 210 – 160 = 50 cm2.

Then the area of one base will be 50/2 = 25 cm2.

Then the side of the base of the prism will be equal to √25 = 5 cm.

Let’s find the area of one side surface. 160/4 = 40 cm2.

Then the height of the prism will be: h = 40/5 = 8 cm.

Answer: The side of the base is 5 cm, the height is 8 cm.