At the base of the rectangular parallelepiped is a square. Find the height of the parallelepiped

At the base of the rectangular parallelepiped is a square. Find the height of the parallelepiped if its total surface area is 160 cm2 and the side surface area is 128 cm2.

Knowing the total area of the prism and the area of the lateral surface, we determine the area of the bases of the prism.

Sb = S floor – S side = 160 – 128 = 32 cm2.

Then the area of the square ABCD will be equal to: Savsd = Sosn / 2 = 32/2 = 16 cm2.

Since there is a square at the base of the prism, AB = BC = CD = AD = √Savsd = √16 = 4 cm.

The area of the lateral surface of the prism is: Sbok = P * AA1, where P is the perimeter of the base.

Side = 4 * AB * AA1.

AA1 = S side / 4 * AB = 128/4 * 4 = 8 cm.

Answer: The height of the prism is 8 cm.