The base of a rectangular parallelepiped with a side edge of 8 m is a rhombus

The base of a rectangular parallelepiped with a side edge of 8 m is a rhombus with diagonals of 10 m and 24 m. Find the full surface of the parallelepiped.

Let us determine what the side of the rhombus will equal, which lies at the base of our right parallelepiped, when it is precisely known from the condition of the problem that its diagonals are equal to 10 m and 24 m:

10: 2 = 5;

24: 2 = 12;

√ (52 + 122) = √ (25 + 144) = √169 = 13.

Determine the area of the rhombus:

10 * 24: 2 = 120.

Let us determine what the area of one side face will be equal to if the side edge is 8 meters:

13 * 8 = 104.

Then the total surface area of our figure is:

4 * 104 + 2 * 120 = 416 + 240 = 656.

Answer: 656 m2.