Question

Find the surface area of the triangular prism. Write your answer as an exact decimal.

Answer 1

`857.6m^2`

Step-by-step explanation

To find the surface area of the prism, we have to find the area of each face of the prism, then find their sum.

The faces of the prism are:

NOTE: Face A appears twice, so we have to double its area when finding the sum.

FACE A

This is a triangle, so its area is:

`\begin{gathered} A=(1)/(2)\cdot b\cdot h \\ A=(1)/(2)\cdot7\cdot9 \\ A=31.5m^2 \end{gathered}`

FACE B

This is a rectangle, so its area is:

`\begin{gathered} A=L\cdot W \\ A=29\cdot7 \\ A=203m^2 \end{gathered}`

FACE C

Its area is:

`\begin{gathered} A=29\cdot9 \\ A=261m^2 \end{gathered}`

FACE D

Its area is:

`\begin{gathered} A=29\cdot11.4 \\ A=330.6m^2 \end{gathered}`

Therefore, the surface area of the triangular prism is:

`\begin{gathered} A=(2\cdot31.5)+203+261+330.6 \\ A=857.6m^2 \end{gathered}`