At the base of a straight prism there is a right-angled triangle, the legs of which are 6 cm and 8 cm

At the base of a straight prism there is a right-angled triangle, the legs of which are 6 cm and 8 cm. Lateral edge of the prism 12. Find the total surface area of the prism and its volume.

By the Pythagorean theorem, we define the hypotenuse of a right-angled triangle at the base of the prism.

AC ^ 2 = 6 ^ 2 + 8 ^ 2 = 100. AC = 10 cm.

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

Sside = P * h = (6 + 8 + 10) * 12 = 288 cm2.

Determine the area of the base of the prism. Sb = 6 * 8/2 = 24 cm2.

Then Sпов = Sbok + 2 * Sсн = 288 + 48 = 336 cm2.

V = Sbn * h = 24 * 12 = 288 cm3.

Answer: Spov = 336 cm2, V = 288 cm3.