Question

Find the area of a regular hexagon with a side measured 6 cm.

Answer 1

area of an equilateral triange of 6 cm X6

Answer 2

The formula for area of a regular polygon is
pa/2 = nas/2
where
p=perimeter
n=number of sides
s=side length (so p=ns)
a=apothem, which is the height of the triangle formed by a side and the centre

Answer 3

Do you know the interior angle (x) of a hexagon?

Answer 4

No.

Answer 5

The interior angle x of a n-sided polygon is 180-360/n.
For n=6 (hexagon), the interior angle would be 180-360/6=120 degrees.
Therefore the triangle formed by one side of the hexagon is an equilateral triangle.

Answer 6

243 cm2

Answer 7

So what you need to find is the apothem (a) and use the standard formula for the regular polygon.
Are you able to find "a", knowing that OAB is an equilateral triangle and using Pythagoras theorem?

Answer 8

Not sure how to.

Answer 9

using a angle u can solve the apotem if theres no given distance @Hedy

Answer 10

isoceles triangle i think

Answer 11

Consider right triangle ODB, then
\(a^2+(s/2)^2=s^2 \) (Pythagoras theorem)
Can you now solve for a knowing that s=6.

Answer 12

Im right mathmate?

Answer 13

@melmel that would be one way to do it if she knows trigo.