The volume of a prism which has an altitude of 10 units and has a right triangle base with a hypotenuse of 13 units and a leg of 12 units is what?

First find area of base:

hypotenuse = 13
one leg = 12
other leg = √(13²-12²)=5
Area of base = 5*12/2=30 unit²

Volume of prism
=(area of base)*height/3
=?

I didn't see where the solid was a pyramid. Usually a prism is a right prism, so the

v = (area of base)*height

To find the volume of a prism, you need to multiply the area of the base by the altitude. In this case, the base of the prism is a right triangle.

To find the area of a right triangle, you can use the formula: A = (1/2) * base * height.

Given that the hypotenuse is 13 units and one leg is 12 units, you can use the Pythagorean theorem to find the other leg. The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the legs.

By substituting the given values into the equation, you can solve for the unknown leg:

13^2 = 12^2 + leg^2
169 = 144 + leg^2
leg^2 = 169 - 144
leg^2 = 25
leg = √25
leg = 5

Therefore, the height of the right triangle base is 5 units.

Now you can calculate the area of the right triangle base using the formula:
A = (1/2) * base * height
A = (1/2) * 12 * 5
A = 30 square units

Finally, you can find the volume of the prism by multiplying the area of the base by the altitude:
Volume = A * altitude
Volume = 30 * 10
Volume = 300 cubic units

Thus, the volume of the prism is 300 cubic units.