How Do You Find The Area Of An Octagon?

7 Answers

Anonymous Profile
Anonymous answered
1/2*a*p.
A=apothem.
P=perimeter.
The apothem is technically the radius of a regular polygon.
...
At least this is what I learned.
:)
but I hope it helps.
Rajesh Shri Profile
Rajesh Shri answered
Octagon is a closed figure with eight sides. It can be a regular octagon where the sides are equal in length or an irregular octagon with unequal sides. We do have to know something to work this out. I will assume we know the length of a side. Say it is 'S'. Now the sum of internal angles for an octagon is 1080 degree and hence each of the internal angle is 135 degree. Now let us assume a square around the octagon. We get 4 triangles at four corners of the octagon in doing this. Let us assume that the right angled triangles have sides that are 'A' units. The area of each such triangle will be ½ base x height hence ½ AxA =1/2 A2 .
Hence the area of the octagon will be (S+2A)*(S+2A) – 4*1/2 A2 . Hence if we know the side of the Octagon and the width of the octagon, we can easily find the area of the regular octagon.
Anonymous Profile
Anonymous answered
I am going to assume that you have a regular octagon and that the width is 12 feet (w in the diagram below). I am going to think of this octagon as a square with the four corners cut off as in the diagram.


The four pieces cut off can be arranged into two squares with sides of length b feet and hence the area of the octagon is
w 2 - 2 b 2 square feet.
Since w = 12 feet, all that is needed is to find b.
From the diagram
w = b + S + b = S + 2b.
Also each of the cut off pieces is a right triangle and hence, by Pythagoras' Theorem,
S 2 = b 2 + b 2 = 2 b 2
Thus

or

Hence the area is
square feet
which is approximately 119 square feet.
Lily James Profile
Lily James answered

An Octagon is a common geometrical figure. It is basically a polygon which has eight sides. It has 8 vertices and the internal angle is 135 degree.

The simplest formula for finding the area of an Octagon is:

A = S2 - B2

Here S is the second shortest diagonal or span of Octagon
and B is length of one of the side or the base of octagon.

Anonymous Profile
Anonymous answered
Find the area of a regular octagon that has an apothem of 6 inches and sides of 10 inches?
Aun Jafery Profile
Aun Jafery answered
This is pretty simple. The octagon can be segregated into eight equal triangles. The area of each triangle can be measured individually and multiplied by eight. Since the octagon is divided into eight triangle the angle formed at the top of each triangle will be 45° as 360/8=45. Now each triangle that is derived can be turned into a pair of right angle triangles by drawing a vertical line from the centre of the octagon/top of the triangle to its side/base. This is also the height of the triangle and the length of this can be easy calculated using trigonometry. Simply apply the formula tan (45/2) = (N/2)/h. Once the base and height are known the area of each triangle can be found using 1/2×base×height. Then the area of the triangle can be multiplied by eight, and voila! You have what you need.

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