# Find the area of the lateral surface of a straight prism at the base of which a rhombus

**Find the area of the lateral surface of a straight prism at the base of which a rhombus with a diagonal of 10 and 24 cm lies, and its lateral edge is 20.**

1. The diagonals of the rhombus are perpendicular and the intersection point is divided in half, therefore, the rhombus is divided into four equal right-angled triangles. To determine the sides of the rhombus, we use the Pythagorean theorem:

a = √ ((10/2) ^ 2 + (24/2) ^ 2) = √ (5 ^ 2 + 12 ^ 2) = √ (25 + 144) = √169 = 13 (cm).

2. The perimeter of a rhombus is equal to four times the value of its side:

Rosn. = 4a = 4 * 13 = 52 (cm).

3. The area of the lateral surface of a straight prism is equal to the product of the height of the prism and the perimeter of its base:

S side. = h * Psc = 20 * 52 = 1040 (cm ^ 2).

Answer: S side. = 1040 cm ^ 2.