Question

Find the volume of the triangular prism.

Answer 1

4.5 ft³

Explanation:

Volume = base area × height

For base area, find one angle using cosine law

18 inch = 18/12 = 1.5ft

1.5² = 2.5² + 2² - 2(2)(2.5)cos(theta)

cos(theta) = 0.8

sin(theta) = sqrt(1 - 0.8²)

sin(theta) = 0.6

Base area:

½ × 2 × 2.5 × 0.6

1.5

Volume = 1.5 × 3

= 4.5 ft³

Answer 2

4.5 ft³

Explanation:

18 inches = 18 × (1/2) ft

= 1.5 ft

since, this is a right triangle according to the given figure then:

the area of the base (triangle) = 2 × 1.5 = 3 ft²

therefore

the volume = 1.5 × 3

= 4.5 ft³