At the base of a straight triangular prism is a right-angled triangle with a 12 cm leg and a 13 cm

At the base of a straight triangular prism is a right-angled triangle with a 12 cm leg and a 13 cm hypotenuse. The lateral edge of the prism is 10 cm, calculate the volume of the prism.

At the base of the prism lies a right-angled triangle ABC, and which leg AB = 12 cm, hypotenuse AC = 13 cm, then, according to the Pythagorean theorem, the leg BC will be equal to:

BC ^ 2 = AC ^ 2 – AB ^ 2 = 13 ^ 2 – 12 ^ 2 = 169 – 144 = 25.

BC = 5 cm.

Then the area of the base of the prisms will be equal to:

Sbn = AB * BC / 2 = 12 * 5/2 = 30 cm2.

Determine the volume of the prism:

V = Sosn * H, where H is the lateral edge of the prism.

V = 30 * 10 = 300 cm3.

Answer: The volume of the prism is 300 cm3.