Mathematics Question and Solution
Notice;
Single interior angle of a regular polygon with 6 sides (regular hexagon) is 120°.
The formula to get it is;
(180°(n-2))/n.
Where n is the side number of the regular polygon.
It implies;
Blue area will be;
Area regular hexagon with single interior angle and single side length 120° and 6cm respectively - 6(area sector of interior angle and radius 120° and 3cm respectively.
= ¼((36x6)/tan(180/6)) - 6((120x9π)/360)
= (54/tan30) - 18π
= 54√(3) - 18π
= 18(3√(3)-π) cm².
Or
Blue area will be;
Area regular hexagon with single interior angle and single side length 120° and 6cm respectively - 2(area circle of radius 3cm)
= ¼((36x6)/tan(180/6)) - 2(3²π)
= (54/tan30) - 18π
= 54√(3) - 18π
= 18(3√(3)-π) cm².
