Answer:
The surface area of the prism is ![1,664\ mm^{2}](https://tex.z-dn.net/?f=1%2C664%5C%20mm%5E%7B2%7D)
Step-by-step explanation:
we know that
The surface area of the triangular prism is equal to
![SA=2B+PL](https://tex.z-dn.net/?f=SA%3D2B%2BPL)
where
B is the area of the triangular face
P is the perimeter of the triangular face
L is the length of the triangular prism
<em>Find the area of the triangular face B</em>
![B=\frac{1}{2}(24)(16)= 192\ mm^{2}](https://tex.z-dn.net/?f=B%3D%5Cfrac%7B1%7D%7B2%7D%2824%29%2816%29%3D%20192%5C%20mm%5E%7B2%7D)
<em>Find the perimeter of the triangular face P</em>
![P=(24+20+20)= 64\ mm](https://tex.z-dn.net/?f=P%3D%2824%2B20%2B20%29%3D%2064%5C%20mm)
we have
![L=20\ mm](https://tex.z-dn.net/?f=L%3D20%5C%20mm)
substitute the values
![SA=2(192)+(64)(20)=1,664\ mm^{2}](https://tex.z-dn.net/?f=SA%3D2%28192%29%2B%2864%29%2820%29%3D1%2C664%5C%20mm%5E%7B2%7D)