# The base of a straight prism is a right-angled triangle with 6 and 8 cm legs.Find the area of the lateral

August 30, 2021 | education

| **The base of a straight prism is a right-angled triangle with 6 and 8 cm legs.Find the area of the lateral surface of the prism if its largest lateral edge is a square**

The triangle at the base will have a hypotenuse C:

C = √ (6 ^ 2 + 8 ^ 2) = √100 = 10 cm;

The hypotenuse is the largest side of a right-angled triangle. The largest side of the triangle will be the side of the largest face of the prism, which is a square. The side of the square is 10 cm, hence the height of the prism is h = 10 cm.

Find the perimeter p of the triangle at the base:

p = 6 cm + 8 cm + 10 cm = 24 cm.

The area S of the lateral surface of the prism:

S = ph = 24 * 10 cm = 240 cm2.

Answer: 240 cm2.