The lateral surface area of the triangular prism is [tex]379.5 sq.units[/tex]
Explanation:
The side lengths of the base of the triangular prism are 5 meters, 8 meters, and 10 meters.
It is given that the height of the prism is 16.5 meters.
To determine the lateral surface area of the prism, let us use the formula [tex]LSA=(a+b+c) h[/tex]
where a, b,c are the side lengths of the base of the triangular prism and h is the height of the prism.
Here [tex]a=5, b=10, c=8[/tex] and [tex]h=16.5[/tex]
Substituting these values in the formula, we have,
[tex]LSA=(5+10+8)16.5[/tex]
Simplifying, we get,
[tex]LSA=(23)16.5[/tex]
Multiplying, we get,
[tex]LSA=379.5[/tex]
Thus, the lateral surface area of the triangular prism is [tex]379.5 sq.units[/tex]
