Answer:
D. [tex]504\text{ units}^2[/tex]
Step-by-step explanation:
We have been an image of a right prism. We are asked to find the surface area of our given prism.
We will use surface area of prism formula to solve our given problem.
[tex]\text{Surface area of right prism}=p\cdot h+2B[/tex], where,
p = Perimeter of base of prism,
h = Height of prism,
B = Area of base of prism.
Now, we need to find the third side of triangular base of prism using Pythagoras theorem.
[tex]x^2=8^2+6^2[/tex]
[tex]x^2=64+36[/tex]
[tex]x^2=100[/tex]
[tex]x=\sqrt{100}[/tex]
[tex]x=10[/tex]
Upon substituting our given values in above formula we will get,
[tex]\text{Surface area of right prism}=(10+8+6)\cdot 19+2(\frac{1}{2}\times 6\times 8)[/tex]
[tex]\text{Surface area of right prism}=(24)\cdot 19+(48)[/tex]
[tex]\text{Surface area of right prism}=456+(48)[/tex]
[tex]\text{Surface area of right prism}=504[/tex]
Therefore, the surface area of our given prism is 504 square units and option D is the correct choice.
