Question

Find the area of regular pentagonal arena whose side is 10 meters. Express ur answer in square feet

Answer 1

Given:

The side of a pentagonal arena is 10 meters.

The objective is to find the area of the arena in square feet.

Step-by-step explanation:

The unit of side from meter to feet can be converted as,

`\begin{gathered} a=1m=10.7639\text{ fe}et \\ a=10m=107.639\text{ fe}et \end{gathered}`

To find area:

The area of pentagonal arena can be calculated as,

`A=(1)/(4)\sqrt[]{5(5+2\sqrt[]{5)}}* a^2\text{ . . . . . . . (1)}`

Now, substitute the value of a in equation (1).

`\begin{gathered} A=(1)/(4)\sqrt[]{5(5+2\sqrt[]{5)}}*(107.639)^2 \\ =\text{ }(1)/(4)(6.82)*(107.639)^2 \\ =1.72*(107.639)^2 \\ =19933.716669\ldots\ldots \\ \approx19933.72\text{ square f}eet \end{gathered}`

Hence, the area of the pentagonal arena is 19933.72 square feet.