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Easy: Apothem and perimeter given
A regular polygon splits into identical triangles meeting at the center. Each has the apothem (the distance from the center to the middle of a side) as its height, so the area is ½ × apothem × perimeter. A regular hexagon is six equilateral triangles, and its apothem is the side times √3 ÷ 2.
Find the area.
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The distance from the centre of a regular polygon to the midpoint of a side, perpendicular to that side. Area = ½ × apothem × perimeter.
A regular hexagon is six equilateral triangles, and each has area (√3/4)s². Six of them give (3√3/2)s².
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