Answer:
The volume of the prism = 27√3/2 inches³ (≅ 23.38 inches³)
Step-by-step explanation:
* Lets revise the volume of the triangular prism
- The prism has 5 faces
- Two triangular bases
- Three rectangular side faces
- The rule of its volume = Area of its base × its height
* Now lets solve the problem
- The bases of the prism are equilateral triangles of side 3 inches
- The side faces of the prism are rectangles of dimensions 3 and 6 inches
∵ Its volume = Area of the its base × its height
- The bases are equilateral triangles
∵ The area of the equilateral triangle = √3/4 s² , where s is the
length of its side
∵ The length of the side = 3 inches
∴ The area of the base = √3/4 (3)² = 9√3/4 inches²
∵ Its height = 6 inches
∴ Its volume = 9√3/4 × 6 = 27√3/2 inches³
* The volume of the prism = 27√3/2 inches³ (≅ 23.38 inches³)
