Question

The triangular prism below has a equilateral triangular bases which side of four and a height of 4.5 inches and rectangular sides measuring for in by 7 inches what is the lateral surface area of the prism?

Answer 1

Lets draw a picture of each part of the given figure:

So, the surface area is the sum of of the area of 3 equal rectangles and 2 equal triangles. The area of a triangle is:

`A_T=(1)/(2)\text{base}* height`

in our case, we have

`A_T=(1)/(2)(4)(4.5)`

which gives

`\begin{gathered} A_T=2*4.5 \\ A_T=9in^2 \end{gathered}`

On the other hand, the area of a rectangle is

`A_R=\text{base}* height`

in our case we get

`\begin{gathered} A_R=(7)(4) \\ A_R=28in^2 \end{gathered}`

Then, the surface area is given by

`A=2\cdot A_T+3\cdot A_R`

That is

`A=2(9)+3(28)`

Then, the answer is

`A=18+84=102in^2`

which corresponds to option 3