Multiple choice

Regular pentagons are inscribed in two circles of radius $5$ and $2$ units respectively. The ratio of their areas is -

  1. $\dfrac 52$
  2. $\dfrac {25}{4}$
  3. $\dfrac {25}{4}\sin 72^0$
  4. $\dfrac {25}{4}\cos 36^0$
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B Correct answer
Explanation

The area of a regular polygon inscribed in a circle of radius R is proportional to R^2. The ratio of areas is (5^2) / (2^2) = 25/4.

AI explanation

The area of a regular polygon inscribed in a circle is proportional to the square of the circle's radius because the area formula involves the square of the radius. Therefore, the ratio of the areas of the two regular pentagons is the square of the ratio of their radii. Calculating this gives 5 squared divided by 2 squared, resulting in 25 divided by 4.

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