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:

$A_T=\frac{1}{2}\text{base}\times height$

in our case, we have

$A_T=\frac{1}{2}(4)(4.5)$

which gives

$\begin{gathered} A_T=2\times4.5 \\ A_T=9in^2 \end{gathered}$

On the other hand, the area of a rectangle is

$A_R=\text{base}\times height$

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