Find the volume of the pyramid if its base is a right-angled triangle with legs 3 and 4 dm, and the height of the pyramid is twice

Let’s call the triangle at the base ABC, where AB, BC are legs, AC is the hypotenuse, then we find the length of AC by the Pythagorean theorem:
AB ^ 2 + BC ^ 2 = AC ^ 2;
9 + 16 = 25;
AC = 5 dm.
We know that the height of the pyramid is twice the length of the hypotenuse, then the length of the height is:
5 * 2 = 10 dm.
The volume of the pyramid is:
V = (1/3) * S * h.
Find the area of the triangle (S):
S = (1/2) * AB * BC = (1/2) * 3 * 4 = 6 dm2.
Let’s find the volume of the pyramid:
V = (1/3) * 6 * 10 = 20 dm3.
Answer: 20 dm3 is the volume of the pyramid.