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

Answer in complete sentences and include all relevant calculations.

What Is The Area Of A Regular Dodecagon With 11inch Sides Answer In Complete Sentences And Include All Relevant Calculations class=

Sagot :

sqdancefan

Answer:

  1354.7 square inches

Step-by-step 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

Answer:

[tex]Area = 1353.9 \: {inches}^{2} [/tex]

Step-by-step explanation:

Hint :

Area of a Regular Dodecagon

A = [tex]3 {s}^{2} (2 + \sqrt{3} )[/tex]

Answer :

The area of a regular dodecagon with 11-inch sides = [tex]3 {(11)}^{2} (2 + \sqrt{3} )[/tex]

[tex]Area = 3( {11)}^{2} (2 + \sqrt{3}) \\ = 3 \times 121 \times 3.73 \\ = 1353.9 \: {inches}^{2} [/tex]

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