Option C: [tex]384 \ in^2[/tex] is the surface area of the prism
Explanation:
Given figure is a triangular prism.
We need to determine the surface area of the triangular prism.
The formula to find the surface area of the triangular prism is given by
[tex]S A=b h+(s 1+s 2+s 3) H[/tex]
where b is the base of the triangle,
h is the height of the triangle,
[tex]s1,s2,s3[/tex] are the three sides of the triangle and
H is the height of the prism.
Let us substitute the values [tex]b=16[/tex] , [tex]h=6[/tex] , [tex]s1=16[/tex] , [tex]s2=10[/tex] , [tex]s3=10[/tex] and [tex]H=8[/tex] in the formula, we get,
[tex]SA=16(6)+(16+10+10)(8)[/tex]
Simplifying, we get,
[tex]SA=96+(36)(8)[/tex]
Multiplying the term, we get,
[tex]SA=96+288[/tex]
Adding the terms, we have,
[tex]SA=384 \ in^2[/tex]
Thus, the surface area of the prism is [tex]384 \ in^2[/tex]
Hence, Option C is the correct answer.
