Given:
The side of a pentagonal arena is 10 meters.
The objective is to find the area of the arena in square feet.
Explanation:
The unit of side from meter to feet can be converted as,
[tex]\begin{gathered} a=1m=10.7639\text{ fe}et \\ a=10m=107.639\text{ fe}et \end{gathered}[/tex]To find area:
The area of pentagonal arena can be calculated as,
[tex]A=\frac{1}{4}\sqrt[]{5(5+2\sqrt[]{5)}}\times a^2\text{ . . . . . . . (1)}[/tex]Now, substitute the value of a in equation (1).
[tex]\begin{gathered} A=\frac{1}{4}\sqrt[]{5(5+2\sqrt[]{5)}}\times(107.639)^2 \\ =\text{ }\frac{1}{4}(6.82)\times(107.639)^2 \\ =1.72\times(107.639)^2 \\ =19933.716669\ldots\ldots \\ \approx19933.72\text{ square f}eet \end{gathered}[/tex]Hence, the area of the pentagonal arena is 19933.72 square feet.
