The base of a rectangular parallelepiped is a rhombus with diagonals equal to 12 cm and 16 cm.

The base of a rectangular parallelepiped is a rhombus with diagonals equal to 12 cm and 16 cm. The total surface area is 532 cm2. Calculate the area of the side face.

We denote the total area of the parallelepiped through S, the area of the lateral surface through S side, and the area of the base through Sсн.

Then S = Sside + 2 x Soсн.

Sside = S – 2 x Soсн.

Since there is a rhombus at the base of the parallelepiped, its area is half the product of its diagonals.

Sсн = (12 x 16) / 2 = 96 cm2.

Then S = 532 – 2 x 96 = 340 cm2.

Answer: The area of the lateral surface of the parallelepiped is 340 cm2.