Question

Find the area of a regular hexagon with apothem 3 square root 3 mm. Round to the nearest whole number.

Answer 1

Side = apothem*2/ sqr rt 3
Side = 6
Perimeter = 6 * 6
Area = (1/2)(perimeter)(apothem)
Area= (1/2)(36)(3\/3)
Area = 93.53

Answer 2

Explanation:

Given is a regular hexagon with apothem 3 square root 3 mm.

We have hexagon regular can be divided into 6 equilateral triangles with common vertex at the centre of the hexagon

Each equilateral triangle will have
`3√(3)` as apothem

Hence using equilateral triangle property

we have side = a (say)

Then
`√(3) (a)/(2) =3√(3) \\Or a = 6`

Area of each triangle = 1/2 bh = 9 sqrt 3

Hence area of hexagon =
`6(9√(3))=54√(3)`

Use sqroot 3 = 1.732

we get

93.53 square mm.