Need with finding the volume of a right triangular prism

The volume of the right triangular prism is 55.4 inches³

Step-by-step 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