How can i work out the area of a nonagon?

Question

How can i work out the area of a regular nonagon given that each side is 0.8m long?

Answer 1

I think I'd start with 9 isosceles triangles.

Each angle at the apex is 360 divided by 9 degrees

=40degrees.

The other two angles are equal, so subtract 40 degs from 180 degs and halve what's left.

Each base angle of the triangle = 70 degs.

You already have 40degs and the side opposite it (0.80m)

So you can use a over sinA = b over sinB to find the other two (equal) sides of the isosceles triangle.

Now drop a perpendicular from the apex of the isosceles triangle to the (middle of) its base, forming two right angled triangles.

Each of these triangles is half of the isosceles triangle.
(remember the base of the right angled triangle is half the 0.80m)

Now you can use

sin = opp/hyp, cos = adj/hyp, tan = opp/adj to find the length of the perpendicular height.

Nearly there!

Area of a triangle = half the base times perpendicular height

When you've worked this out for one of the isosceles triangles, you just have to remember back in line one, that you are finding the area of 9 identical triangles, so you multiply the area of one by 9 to get the area of the nonagon.

This uses lots of fairly sinple steps, which you should be able to remember in an exam. PS don't try to remember the order of the steps we used here, just have confidence that when you start, the solution will unfold for you. If you wanted to practice, try it in a week with a different polygon!

Answer 2

yes
Divide nonagon into 9 triangles
The angles of each of these triangles is A(40),
(B)60 ,(C)60
And side opposite to 40 degree is 0.8
Drop a perpendicular AD from A on BC
And using trigonometry
Tan60=AD/0.4
AD=0.4*tan60
So area of triangle ABC
=(0.4*tan60*0.8)/2
area of nonagon=9*area of ABC

Answer 3

Area of a regular polygon
A=[1/4]*n*b^2 cot Pi/n
b=length of a side
n=number of sides.
A=1/4*9*.8^2*cot Pi/9
=1.53 cot .35rad
=1.53*2.74
=4.19m^2

Answer 4

if its that big get inside with a tape measure.

Answer 5

Try here: