Question

Perimeter of hexagon and n sided polygon is the same. The side of hexagon is 2 times the side of n sided polygon. Find the ratio between interior angle of the hexagon and the interior angle of n sided polygon.
1. 5 : 4
2. 4 : 5
3. 1 : 2
4. 2 : 1

Answer 1

Correct Answer - Option 2 : 4 : 5

Calculation:

Perimeter of hexagon = 6 × side of hexagon

Perimeter of n sided polygon = n × side of polygon

⇒ 6 × side of hexagon = n × side of polygon

⇒ n = 6 × 2 = 12

Interior angle of hexagon = (6 - 2) × 180/6 = 120°

Interior angle of 12 sided polygon = (12 - 2) × 180/12 = 150°

∴ Required ratio = 120° : 150° = 4 : 5

Both perimeters are equal and ratio of their sides is given so we can find a number of sides of other polygon.

Interior angle of n sided polygon = (n - 2) × 180°/n