The lateral area of a right prism is L=P h, where P is a perimeter of the base and h is the height of the prism. The surface area of the prism is S=L+2B, where B is the area of the base.
A cereal container can be modeled by the following right rectangular prism with a length of l= 18.6 cm, a width of w= 7 cm, and a height of h= 29 cm.
We are asked to find the lateral and the surface area of the container and round the answers to the nearest tenth if necessary. The lateral area of a right prism is $L=\textcolor{darkorange}{P}\colIII{h},$ where $\textcolor{darkorange}{P}$ is the perimeter of the base. This tells us that $\textcolor{darkorange}{P}=2\t\col{18.6}+2\t\colII{7}=\textcolor{darkorange}{51.2}$ centimeters. Now, let's find $L!$
The lateral area is $\textcolor{darkviolet}{L}=\textcolor{darkviolet}{1484.8}$ square centimeters. The surface area of the prism is $S=\textcolor{darkviolet}{L}+2\textcolor{violet}{B},$ where $\textcolor{violet}{B}$ is the area of the base. Since the base is a rectangle that is $\col{18.6}$ cm by $\colII{7}$ cm, its area is $\textcolor{violet}{B}=\col{18.6}\t\colII{7}=\textcolor{violet}{130.2}$ square centimeters. Finally, let's find the surface area of the container.
