# At the base of a straight prism, a rhombus with diagonals equal to 16 cm and 30 cm.

**At the base of a straight prism, a rhombus with diagonals equal to 16 cm and 30 cm. Determine the area of the lateral surface of the prism if its volume is 4800 cm ^ 3**

Let’s define the area of the base ABCD, which is a rhombus.

Savsd = АС * ВD / 2 = 16 * 30/2 = 240 cm2.

Knowing the volume of the prism and the area of the base, we determine the height of the prism.

V = Savsd * AA1.

AA1 = V / Savsd = 4800/240 = 20 cm.

The diagonals of the rhombus intersect at right angles and are divided in half at the point of intersection, then AO = AC / 2 = 30/2 = 15 cm, DO = BD / 2 = 16/2 = 8 cm.

Then in a right-angled triangle AOD, AD ^ 2 = AO ^ 2 + DO ^ 2 = 225 + 64 = 289.

AD = AB = BC = CD = 17 cm.

Let us determine the area of the lateral surface. Sside = AA1 * Ravsd = 20 * 68 = 1360 cm2.

Answer: The lateral surface area is 1360 cm2.