Question

Find the T.A. for the prism and also find the L.A. for the prism

Answer 1

use bh + (S1+ S2 + S3)H to find the T.A.
Triangle: base 'b', height 'h', and sides S1, S2 and S3
use L=Ph to find L.A. (the surface area of all sides, or faces, that are not the base)
L= the lateral area of the prism, P= the perimeter of one base, h= the height of the prism

Answer 2

The total area of a prism is

`A=ph +2B`

Where
`p` is the perimeter of the base,
`h` is the height of the prims and
`B` is the area of the base.

Remember that the perimeter is the sum of all side. So, first we need to find the hypothenuse of the base triangle.

`h^(2)=4^(2) +6^(2)\\ h=√(16+36) =√(52) \approx 7.2`

Now, the perimeter of the base is

`p=7.2+6+4=17.2`

Also, the height of the prism is
`h=8`, and the area of the base is

`B=(1)/(2)4(6)=12`

Then, we replace all values,

`A=17.2(8)+2(12)=137.6+24=161.6`

So, the total area of the prism is 161.6 square units, approximately.

Now, the lateral area is defined as
`L=ph`, replacing all values, we have

`L=17.2(8)=137.6`

So, the lateral area is 137.6 square units, approximately.