Question

Use the net to find the surface area of the prism 8in 15in 17in 9in

Answer 1

The surface area of the prism is 480 in².

Explanation:

Given:

The prism dimensions are 8in 15in 17in and 9in.

Now, to find the surface area:

So, to get the surface area we put formula:

a=8in, b=15in, c=17in and h=9in.

Surface area = 2A+(a+b+c)h.

Whereas,
`A=√(s(s-a)(s-b)(s-c))`

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

Now, we find s first:

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

`s=(8+15+17)/(2)`

`s=(40)/(2)=20.`

Then, we get A :

`A=√(s(s-a)(s-b)(s-c))`

`A=√(20(20-8)(20-15)(20-17))`

`A=√(20(12)(5)(3))`

On solving we get:

`A=√(3600)=60.`

Now, putting the value of A in the formula to get the surface area:

`Surface area = 2A+(a+b+c)h.`

`Surface area = 2* 60+(8+15+17)9.`

`Surface area = 120+(40)9.`

`Surface area = 120+360.`

`Surface area = 480\ in^2.`

Therefore, the surface area of the prism is 480 in².