Question

What is the area of a regular dodecagon with 11-inch sides?

Answer in complete sentences and include all relevant calculations.

Answer 1

`Area = 1353.9 \: {inches}^(2)`

Explanation:

Hint :

Area of a Regular Dodecagon

A =
`3 {s}^(2) (2 + √(3) )`

Answer :

The area of a regular dodecagon with 11-inch sides =
`3 {(11)}^(2) (2 + √(3) )`

`Area = 3( {11)}^(2) (2 + √(3)) \\ = 3 * 121 * 3.73 \\ = 1353.9 \: {inches}^(2)`

Hope it is helpful....

Answer 2

1354.7 square inches

Explanation:

The area of a regular n-sided polygon with side length s can be found using the formula ...

A = n·s²/(4·tan(180°/n))

For n=12 and s=11, the area is ...

A = (12(11²)/(4·tan(15°)) ≈ 1354.7 . . . . square inches