Suppose I have a regular pentagon of side lengths 10 units.
I want to calculate its area.
So this is what I did firstly without using any formula...
I split the pentagon into 5 equal triangles from the centre. This creates a triangle with base 10 units and unknown height. Knowing angles in a circle add to 360, I divide 360 by 5 in order to find the top angle of each triangle in the pentagon; the angle closest to the centre of the pentagon. This gave me 72 degrees. Now knowing each triangle is identical since its a regular pentagon, I take 1 triangle and split it into two right angled triangles by cutting it into two from the top. Knowing both these are the same since its original lengths on the sides were the same - isosceles I now have a right angled triangle, I also halve 72 to get 36 for the top angle and split the 10 in half to get 5 for the side length on the bottom. Now to find the height of this triangle I use tan(36) = 5/x where x is the height. I rearrange this to form x = 5/tan(36). Now I calculate the height to be 0.64512209139. Firstly this doesn't seem right for the height marked x but if I continue you'll realise its wrong according to the original formula. 0.64512209139 * (10/2) = 3.22561045699 (The area of 1 of the triangles in the pentagon). This multiplied by 5 so: 3.22561045699 * 5 = 16.13units^2 (2dp). Now I don't know if I did anything wrong but the correct area equates to 172.05...
How does this. work please explain where I went wrong...