Answer:
The volume of the prism = 300 units³
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