Question

# Kim is building a large gazebo for her backyard. It is in the shape of a regular hexagon. Each side of the gazebo is 12 feet long. The apothem is 10.4 feet. She needs to purchase stones for the floor. It costs \$9.50 per square foot for a special type of interlocking stone. Find the cost of the gazebo's floor. Round to the nearest ten dollars.

Solution

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Determine the area of the given gazebo with the shape of a regular hexagon. Let $a$ be the apothem and $p$ be the perimeter.

\begin{align*} A &= \dfrac{1}{2}ap && \text{Write the equation}\\ A &= \dfrac{1}{2}(10.4)(12 \cdot 6) && \text{Substitute the values}\\ A &= \dfrac{1}{2}(10.4)(72) && \text{Multiply the values}\\ A &= 374.4 && \text{Multiply the values} \end{align*}

The area of the gazebo is 374.4 square feet. Determine the cost of the gazebo's floor.

$\begin{gather*} 374.4 \times 9.50 = \3,556.80 = \3560 \end{gather*}$

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