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

Answer:

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.

$h^{2}=4^{2} +6^{2}\\ h=\sqrt{16+36} =\sqrt{52} \approx 7.2$

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

$B=\frac{1}{2}4(6)=12$

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.