Question

18. Find the total surface area of the right triangular prism. .1112

Answer 1

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

`TSA=P\cdot h+2B`

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)

`\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}`

Now we can find the perimeter of the base,

`\begin{gathered} P=s_1+s_2+s_3 \\ P=9+12+15 \\ P=36 \end{gathered}`

The area of the base is given by

`\begin{gathered} B=(1)/(2)\cdot b\cdot h \\ B=(1)/(2)\cdot12\cdot11 \\ B=66 \end{gathered}`

So, the total surface area of the right triangular prism is

`\begin{gathered} TSA=P\cdot h+2B \\ TSA=36\cdot11+2(66) \\ TSA=396+132 \\ TSA=528\: \text{unit}^2 \end{gathered}`

Therefore, the total surface area of the right triangular prism is 528 square units.