Exercise 55 Page 838

Let's analyze the given rectangular cake pan.

We are asked to find the area of the inside of the pan that need to be coated. The bottom of the pan is a rectangle 13 by 9 inches. Therefore, the area of the base is \textcolor{darkviolet}{B_\text{base}}={\color{#0000FF}{13}}\cdot {\color{#009600}{9}}=\textcolor{darkviolet}{117} squared inches. Next we will find the lateral area of the cake pan.

The lateral area of a prism is equal to L=Ph, where P is the perimeter of the base and h is the height of the prism. This tells us that P=2* 13+2* 9= 44 inches, and h= 2 inches.

L=Ph

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Substitute values and evaluate

SubstituteII

P= 44, h= 2

L=( 44)( 2)

L=88

The lateral area is L=88 square inches, and the area of the base is B=117 square inches. Therefore, the area of the inside of the pan that needs to be coated is the sum of these two ares.

A_\text{coated}=\textcolor{darkorange}{L}+\textcolor{darkviolet}{B}

SubstituteII

L= 88, B= 117

A_\text{coated}=\textcolor{darkorange}{88}+\textcolor{darkviolet}{117}

AddTerms

Add terms

A_\text{coated}=205

Finally, we get that the area that needs to be coated is 205 square inches.