How to Find area of a regular Octagon...

[MasterEds]

Hey all,

How would you find the area of an octagon when given only the distance from O (middle) to A.

so if O to A is 5cm, where would you start?

[b^3]

If it is a regular octagon, split it up into equilater triangles, then use herons formula (all the side lenghts will be 5cm) to find the area of a triangle, then times by the number of triangles.

[yawho]

If it is a regular octagon, split it up into equilater triangles, then use herons formula (all the side lenghts will be 5cm) to find the area of a triangle, then times by the number of triangles.

What is a regular octagon?

[b^3]

All sides are equal and all angles are equal, if I remember correctly, sorry I haven't done further in a while.

[paulsterio]

if the side length is L, the area of a regular octagon is (1+sqrt(2)) x L^2

This formula I managed to derive by splitting the octagon up into two trapeziums and a rectangle down the middle, if someone really wants, I can upload an image of my derivation, but basically in your case, L = 5, so the area = 5(1+sqrt(2))

(sqrt = square root of)

[paulsterio]

Sorry, I realised that you're talking about the distance to the centre is 5, in that case, you'll have to calculate the distance of the edge using the cosine rule, with the angle being 45 and the two other sides being 5

so c^2 = 5^2 + 5^2 - 2 x 5 x 5 x cos(45) = 50 - 50cos(45)...etc

[molloyd]

split the octagon into 8 triangles all will be isosceles (Not equilateral hexagons have those) now draw a circle around the tips of the triangles and you will see you have 8 equal angles making up 360  so each is 45.
now use the rule 1/2 x 5 x 5 x sin(45) (non right angled triangle formula) to find the area of one triangle then multiply that by 8 should be like 70.71cm squared or whatever the units are.

[b^3]

split the octagon into 8 triangles all will be isosceles (Not equilateral hexagons have those) now draw a circle around the tips of the triangles and you will see you have 8 equal angles making up 360  so each is 45.
now use the rule 1/2 x 5 x 5 x sin(45) (non right angled triangle formula) to find the area of one triangle then multiply that by 8 should be like 70.71cm squared or whatever the units are.

Yeh sorry isosceles triangles, when I was typing the above up I had to stop and think which of the two it was going to be, I chose the wrong one. My mistake, thanks for correcting that molloyd.

[molloyd]

yer wasn't trying to offend you man no problem and do you mind having a look at my post and im new to the forum my teachers shit so i wouldnt trust her word on the question i have

[b^3]

yer wasn't trying to offend you man no problem and do you mind having a look at my post and im new to the forum my teachers shit so i wouldnt trust her word on the question i have

Yeh thats ok, I didn't take any offence, we all make mistakes. And sorry I don't remember about the rounding in further since I have changed myself to methods and spesh ways and rules this year. Sorry I can't help.

[MicroShift]

EDIT: Wrong topic.. =\