We are asked to find the total surface area of the right triangular prism.
Recall that the total surface area of a right triangular prism is given by
[tex]TSA=P\cdot h+2B[/tex]
Where P is the perimeter of the base, h is the height of the prism, and B is the area of the base.
From the figure, we see that
height = 11
side 1 = 9
side 2 = 12
We can apply the Pythagorean theorem to find the length of the third side. (hypotenuse)
[tex]\begin{gathered} c^2=a^2+b^2 \\ c^2=9^2+12^2 \\ c^2=81^{}+144 \\ c^2=225 \\ c=\sqrt[]{225} \\ c=15 \end{gathered}[/tex]
Now we can find the perimeter of the base,
[tex]\begin{gathered} P=s_1+s_2+s_3 \\ P=9+12+15 \\ P=36 \end{gathered}[/tex]
The area of the base is given by
[tex]\begin{gathered} B=\frac{1}{2}\cdot b\cdot h \\ B=\frac{1}{2}\cdot12\cdot11 \\ B=66 \end{gathered}[/tex]
So, the total surface area of the right triangular prism is
[tex]\begin{gathered} TSA=P\cdot h+2B \\ TSA=36\cdot11+2(66) \\ TSA=396+132 \\ TSA=528\: \text{unit}^2 \end{gathered}[/tex]
Therefore, the total surface area of the right triangular prism is 528 square units.
