A square and a regular hexagon share the same perimeter. What is the ratio of their areas?
Show answer & explanation
Correct answer: A
Explanation
Both have the same perimeter = P
Side of square = P/4
Area of square = (P/4)² = P²/16
Side of hexagon = P/6
Area of hexagon -
= (3√3/2) × (P/6)²
= (3√3/2) × P²/36
= √3P²/24
Square: Hexagon
= (P²/16) : (√3P²/24)
= 24 : 16√3
= 3 : 2√3
≈ 1 : 1.155