In a straight triangular prism, a right-angled triangle with legs 8 cm and 6 cm.

In a straight triangular prism, a right-angled triangle with legs 8 cm and 6 cm. The side edge of the prism is 12 cm. Find the total surface area of the prism.

If the legs of a right-angled triangle are 8 cm and 6 cm, then its hypotenuse is equal to the square root of the sum of squares 8 and 6, that is, 10 cm.

By condition, the prism is rectangular with a side edge of 12 cm, which means that its side faces are three rectangles, the areas of which are

12 * 8 = 96 cm2,

12 * 6 = 72 cm2,

12 * 10 = 120 cm2.

And the areas of the two bases of the prism

8 * 6/2 = 24 cm2.

Thus, the total surface area of the prism is

2 * 24 + 96 + 72 + 120 = 336 cm2.