Answer:
The volume of the right triangular prism is 55.4 inches³
Explanation:
* Lets study the problem
- The triangular prism 5 faces, two triangular base and three
rectangular side faces
- The volume of any prism = Area of its base × its height
- The base of the triangular prism is a triangle
∴ The volume of the triangle prism = Area of the triangle × its height
- In the figure the base is equilateral triangle of side length 4 inches
- The area of the equilateral triangle = √3/4 s², where s is
the length of its side
* we got this area from the rule ⇒ AΔ = (1/2) × s1 × s2 × sinФ,
where Ф is the angle between s1 and s2. In the equilateral Δ
s1 = s2 = s and Ф = 60, then its area = (1/2) × s × s × sin(60),
area of the equilateral Δ = (1/2) × s² × √3/2 = √3/4 s²
∴ The area of the base = √3/4 × (4)² = √3/4 × 16 = 4√3 inches²
* Now we can find the volume of the prism
∵ Area of the base = 4√3 inches²
∵ The length of its height = 8 inches
∵ The volume = area of the base × height
∴ The volume = 4√3 × 8 = 32√3 = 55.4 inches³
* The volume of the right triangular prism is 55.4 inches³