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Matt Nibecker · Answer 1 · 2023-07-12T04:34:58+0000

We want to find the surface area of the prism shown. For doing so, we remember that:

$\begin{gathered} A_s=2A_b+A_l \\ \text{where }A_b\text{ is the area of the base and }A_l\text{ is the lateral area} \end{gathered}$

on this case, we will find the areas:

$\begin{gathered} A_b=(6\operatorname{cm})(9\operatorname{cm})=54\operatorname{cm} \\ 2A_b=108\operatorname{cm} \end{gathered}$

Now, for the lateral area we have:

$\begin{gathered} A_l=2(3cm\cdot9cm)+2(3cm\cdot6cm) \\ =2(27cm^2)+2(18cm^2) \\ =54\operatorname{cm}+36\operatorname{cm} \\ =90\operatorname{cm} \end{gathered}$

And replacing on the formula, we get that:

$\begin{gathered} A_s=2A_b+A_l \\ =108\operatorname{cm}+90\operatorname{cm} \\ =198\operatorname{cm} \end{gathered}$

This means that

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