Question

The surface area of a right triangular prism is 228 square inches. 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 bae is 10 inches. Find the height of the prism.

Please help meeeee!!!!!!

Answer 1

`look\ at\ the\ picture\\\\Area=228\ in^2\\\\Area=2A_1+A_2+A_3+A_4\\\\2A_1=2\cdot(6\cdot8)/(2)=48\ (in^2)\\\\A_2=8H\\\\A_3=6H\\\\A_4=10H`


`48+8H+6H+10H=228\\\\48+24H=228\ \ \ /-48\\\\24H=180\ \ \ /:24\\\\H=7.5\ (in)`

Answer 2

The height of right triangular prism is 7.5 in.

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

`A=(1)/(2)\tims base* height`

`A_1=(1)/(2)\tims 6* 8=24`

Let the height of the prism be h.

Area of a rectangle is

`A=length* width`

`A_2=6* h=6h`

`A_3=8* h=8h`

`A_4=10* h=10h`

The surface area of a right triangular prism is

`A=2* \text{Area of base}+\text{Area of three rectangles}`

`A=2* (A_1)+A_2+A_3+A_4`

`A=2* (24)+6h+8h+10h`

`A=48+24h`

The surface area of a right triangular prism is 228 square inches.

`228=48+24h`

`180=24h`

`h=7.5`

Therefore the height of right triangular prism is 7.5 in.