McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
Practice Test
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Exercise 5 Page 875

Use the formula for the surface area of a pyramid.

56 square centimeters

A tea bag can be modeled by the following square pyramid with a base edge of s= 4 centimeters and a height of l= 5 centimeters.

We are asked to find the surface area of the pyramid, \textcolor{darkorange}{S_\text{tea bag}}. \begin{gathered} \textcolor{darkorange}{S_\text{tea bag}}=\textcolor{darkviolet}{B}+\dfrac{1}{2}{\color{#FF0000}{P}}{\color{#009600}{\ell}} \end{gathered} Here, B stands for the area of the base. Since the base is a square with a side length of s=4 centimeters, the area of the base is B=4^2=16 square centimeters. The variable P is the perimeter of the base. This tells us that P=4* 4= 16 centimeters. Now, let's substitute the values into the formula for \textcolor{darkorange}{S_\text{tea bag}}.
\textcolor{darkorange}{S_\text{tea bag}}=\textcolor{darkviolet}{B}+\dfrac{1}{2}{\color{#FF0000}{P}}{\color{#009600}{\ell}}
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Substitute values and evaluate
\textcolor{darkorange}{S_\text{tea bag}}=\textcolor{darkviolet}{16}+\dfrac{1}{2}({\color{#FF0000}{16}})({\color{#009600}{5}})
\textcolor{darkorange}{S_\text{tea bag}}=16+\dfrac{1}{2}\cdot 80
\textcolor{darkorange}{S_\text{tea bag}}=16+\dfrac{80}{2}
\textcolor{darkorange}{S_\text{tea bag}}=16+40
\textcolor{darkorange}{S_\text{tea bag}}=\textcolor{darkorange}{56}
Therefore, the surface area of the tea bag is 56 square centimeters.