Multiple choice

Find the area of a regular pentagon whose each side measure $6\;cm$ and the radius of the inscribed circle is $4\;cm$.

  1. $60\;cm^2$
  2. $80\;cm^2$
  3. $60\;m^2$

  4. None of these
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A Correct answer
Explanation

The area of a regular polygon is given by the formula Area = (1/2) * perimeter * apothem. The perimeter of a pentagon with side 6 cm is 5 * 6 = 30 cm, and the apothem (radius of the inscribed circle) is 4 cm. Thus, Area = (1/2) * 30 * 4 = 60 cm^2.

AI explanation

The formula for the area of a regular polygon is given by half the product of its perimeter and its apothem, where the apothem is the radius of the inscribed circle. The perimeter of this regular pentagon is 5 times 6 cm, which equals 30 cm. Multiplying this perimeter by the given radius of 4 cm and then dividing by 2 yields an area of 60 cm^2. The area of the regular pentagon is 60 cm^2.

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