Question

Find the surface area of the prism. A drawing of a right triangular prism. The triangular faces have perpendicular sides 5 centimeters and 12 centimeters and the third side is 13 centimeters. The height of the prism is 16 centimeters.

Answer 1

The surface Area of the prism is 540 square centimeters.

Explanation:

Given:

Base side
`a` = 5 cm

Base side
`b` = 13 cm

Base side
`c` = 12 cm

Height of the prism
`h` = 16 cm

We need to find the surface area of the prism.

Solution:

Now we know that;

Given prism is a right angled triangular prism.

The formula for Surface area of triangular prism is given by;

`A=2A_B+(a+b+c)h`

where
`A_B` ⇒ Lateral Surface area.

`A_B=√(s(s-a)(s-b)(s-c))`

`s=(a+b+c)/(2)`

First we will find the value of 's'.

`s= (a+b+c)/(2) =(5+12+13)/(2)=(30)/(2)=15`

Now we will find
`A_B`

`A_B=√(s(s-a)(s-b)(s-c))\\\\A_B= √(15(15-5)(15-13)(15-12))\\\\A_B= √(15* 10*2*3)\\\\A_B=√(900)\\ \\A_B=30\ cm^2`

Now we will find the surface area of the prism
`A`

`A=2A_B+(a+b+c)h`

`A = 2* 30+(5+13+12)16\\\\A=60+30* 16\\\\A=60+480\\\\A=540\ cm^2`

Hence The surface Area of the prism is 540 square centimeters.