Question

Find the surface area of the prism. Round to the nearest tenth if necessary. 5 in. 4 in 10 in. 5 in 6 in.

Answer 1

We are asked to determine the surface area of the given prism. To do that we will add the area of each of the surfaces.

The top and bottom surfaces are triangles. The area of a triangle is given by:

`A_t=(bh)/(2)`

-where

`\begin{gathered} b=\text{ base} \\ h=\text{ height} \end{gathered}`

Since there are two triangles we multiply the area by 2:

`2A_T=2(bh)/(2)=bh`

Now, we plug in the values given in the diagram:

`2A_T=(6in)(4in)`

Solving the operations:

`2A_T=24in^2`

Now we determine the area of the side surfaces.

We use the following division:

The area of a rectangle is given by:

`A_R=bh`

Where:

`\begin{gathered} b=\text{ base} \\ h=\text{ height} \end{gathered}`

For the first rectangle (R1) we have:

`A_(R1)=(6in)(10in)=60in^2`

For the second rectangle we have:

`A_(R2)=(5in)(10in)=50in^2`

For the third rectangle we have:

`A_(R3)=(5in)(10in)=50in^2`

Now, the total surface area is the sum of the areas we have determined:

`A=2A_T+A_(R1)+A_(R2)+A_(R3)`

Plugging in the values:

`A=24in^2+60in^2+50in^2+50in^2`

Solving the operations:

`A=184in^2`

Therefore, the surface area is 184 square inches.