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:

The volume of the prism = 300 units³

Step-by-step explanation:

* Lets study the triangular prism

- The triangular prism has 6 faces

- Two right triangular bases

- Four rectangular side faces

- The volume of the prism = area of its base × its height (altitude)

* Now lets solve the problem

∵ The base is a right triangle with a hypotenuse of 13 units and

   a leg of 12 units

∵ The area of the right triangle = 1/2 × leg1 × leg2

- You can find the length of other leg by using Pythagoras theorem

∵ (hypotenuse)² = (leg1)² + (leg2)²

∵ hypotenuse = 13 units

∵ leg1 = 12 units

∴ (13)² = (12)² + (leg2)²

∴ 169 = 144 +  (leg2)² ⇒ subtract 144 from both sides

∴ 25 =  (leg2)² ⇒ take √ for both sides

∴ leg2 = 5 units

- The area of the right triangle = 1/2 × leg1 × leg2

∴ The area of the base = 1/2 × 12 × 5 = 30 units²

∴ The volume of the prism = 30 × 10 = 300 units³

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step-by-step explanation:

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