Find the volume of the pyramid, at the base of which lies a right-angled triangle with a leg of 5 cm

Find the volume of the pyramid, at the base of which lies a right-angled triangle with a leg of 5 cm, a hypotenuse of 13 cm. The height of the pyramid is 15 cm.

Determine the area of the base of the pyramid.

At the base of the pyramid lies a right-angled triangle ABC, then by the Pythagorean theorem, we determine the length of the leg AB.

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

AB = 12 cm.

Then Savs = AB * BC / 2 = 12 * 5/2 = 30 cm2.

Let’s define the volume of the pyramid.

V = Sbn * DO / 3 = 30 * 15/3 = 150 cm3.

Answer: The volume of the pyramid is 150 cm3.