Answer:
The height of right triangular prism is 7.5 in.
Step-by-step explanation:
The base is a right triangle with a base height of 6 inches and a base length of 8 inches. The length of the third side of the base is 10 inches.
The area of a triangle is
[tex]A=\frac{1}{2}\tims base\times height[/tex]
[tex]A_1=\frac{1}{2}\tims 6\times 8=24[/tex]
Let the height of the prism be h.
Area of a rectangle is
[tex]A=length\times width[/tex]
[tex]A_2=6\times h=6h[/tex]
[tex]A_3=8\times h=8h[/tex]
[tex]A_4=10\times h=10h[/tex]
The surface area of a right triangular prism is
[tex]A=2\times \text{Area of base}+\text{Area of three rectangles}[/tex]
[tex]A=2\times (A_1)+A_2+A_3+A_4[/tex]
[tex]A=2\times (24)+6h+8h+10h[/tex]
[tex]A=48+24h[/tex]
The surface area of a right triangular prism is 228 square inches.
[tex]228=48+24h[/tex]
[tex]180=24h[/tex]
[tex]h=7.5[/tex]
Therefore the height of right triangular prism is 7.5 in.
