# 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.

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