Question

The bases of a prism are right triangles with side lengths 6 meters,

sters, and 10 meters. The height of the prism is 3 meters. What is
who lateral area of the prism? What is the total surface area?

Answer 1

Part a) The lateral area of the prism is
`LA=(48+6√(34))\ m^2`

Part b) The surface area of the prism is
`SA=(108+6√(34))\ m^2`

Explanation:

Part a) What is the lateral area of the prism?

we know that

The lateral area of the prism is

`LA=PH`

where

P is the perimeter of the base

H is the height of the prism

we have

`a=6\ m\\b=10\ m\\H=3\ m`

The perimeter of the base is

`P=a+b+c`

Find the hypotenuse of the right triangle

Applying the Pythagoras Theorem

`c^2=6^2+10^2`

`c^2=136`

`c=√(136)\ m`

`c=2√(34)\ m`

Find the perimeter of the base P

`P=6+10+2√(34)`

`P=(16+2√(34))\ m`

Find the lateral area of the prism

`LA=(16+2√(34))3`

`LA=(48+6√(34))\ m^2`

Part b) What is the total surface area?

The total surface area is

`SA=LA+2B`

where

LA is the lateral area

B is the area of the base

Find the area of the base

Remember that the base is a triangle so

`B=(1)/(2)(a)(b)`

we have

`a=6\ m\\b=10\ m`

substitute

`B=(1)/(2)(6)(10)`

`B=30\ m^2`

Find the surface area of the prism

`SA=LA+2B`

we have

`B=30\ m^2`

`LA=(48+6√(34))\ m^2`

substitute

`SA=(48+6√(34))+2(30)`

`SA=(48+6√(34))+60`

`SA=(108+6√(34))\ m^2`