Exercise 40 Page 42

We will begin with finding the area of the base. We see that the base is a square since it is a rectangle with equal sides. To find its area, we will use the formula for the area of a square, where b is the side length. \begin{gathered} A_\text{base} = {\color{#FD9000}{b}}^2 \end{gathered} The four other sides are also identical — each is a rectangle with a length l and a width b. The formula for the area of a rectangle tells us that the area of a rectangle is the length multiplied by the width. In our case, these lengths are l and b, respectively. \begin{gathered} A_\text{side} = {\color{#A800DD}{\ell}}{\color{#FD9000}{b}} \end{gathered} We can now add add these expressions to write the formula for the surface area S of the prism. Keep in mind there are 2 bases and 4 sides. \begin{aligned} S =\ & 2{\color{#009600}{A_\text{base}}} +4 {\color{#FF00FF}{A_\text{side}}} \\ &\Downarrow \\ S =\ & 2{\color{#009600}{b^2}}+4{\color{#FF00FF}{\ell b}} \end{aligned}