Question
Download Solution PDFThe ratio of the areas of a square and a regular hexagon, both inscribed in a circle is -
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDF
In the above diagram, the diameter of the circle is equal to the length of the diagonal of the square.
⇒ √2a = 2r
⇒ a = √2r
⇒ Area of the square = a2 = (√2r)2 = 2r2
In the above diagram, the radius of the circle is equal to the side of the hexagon.
The hexagon consists of 6 equilateral triangles,
⇒ Area of hexagon = 6 × √3/4 × a2 = 6 × √3/4 × r2
∴ Ratio of areas of a square and hexagon = 2r2 : 6 × √3/4 × r2 = 4 : 3√3Last updated on Jun 11, 2025
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