the apothem of a regular polygon is the perpendicular distance from the centre to one of the sides.
A hexagon is made up 6 equilateral triangles, let's look at one of these
let its base be 2x, then its height is 9cm
and tan 60º = 9/x
x = 9/tan60, and the base of 2x would then be 18/tan60
the area of one triangle is
(1/2)(2x)(9)
= (1/2)(18/√3)(9)
= 81/√3
so the area of the hexagon is 6(81/√3)
= 486/√3
= 162√3 after rationalizing the denominator.
find the area of a regular hexagon with an apothem of 9cm.give answer in simplified radical form?
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