Question

Find the surface area of a right prism whose bases are equilateral triangles with side lengths of 6 in. The height of the prism is 10in

Answer 1

The surface area of the prism is
`(18√(3)+180)\ in^(2)`

Explanation:

we know that

The surface area of the triangular prism is equal to

`SA=2B+PH`

where

B is the area of the triangular base

P is the perimeter of the triangular base

H is the height of the prism

Find the area of the base B

Applying the law of sines to find the area of a equilateral triangle

`B=(1)/(2)b^(2) sin(60\°)`

we have

`b=6\ in`

`sin(60\°)=√(3)/2`

substitute

`B=(1)/(2)6^(2)(√(3)/2)`

`B=9√(3)\ in^(2)`

Find the perimeter P

`P=3*6=18\ in`

we have

`H=10\ in`

substitute the values

`SA=2(9√(3))+(18)(10)=(18√(3)+180)\ in^(2)`