Area of Octagon
The area of octagon is defined as the total amount of area that is enclosed by all octa(eight) sides of the octagon. Octagon is an eightsided polygon. The area of the octagon can be calculated by diving it into 8 equal isosceles triangles. In this minilesson, we will discuss the area of the octagon in detail.
1.  What Is the Area of Octagon? 
2.  How to Calculate Area of Octagon? 
3.  FAQs on Area of Octagon 
What Is the Area of Octagon?
We already read that octagon is a 2dimensional shape with 8 sides. The area of the octagon is the area that is within the eight sides of the octagon. To calculate the area of the octagon we can use the area of an isosceles triangle. We divide the area of the octagon into eight equal isosceles triangles and calculate it accordingly.
The general formula we use to calculate the area of the octagon is:
Area of Octagon Formula
2s^{2}(1+√2), where s is the length of the side of the octagon.
How to Calculate Area of Octagon?
The area of an octagon is 2s^{2}(1+√2). By using the following steps mentioned below we can find the area of the octagon.
 Step 1: Calculate the length of the side of the octagon.
 Step 2: Find the square of the length of the side.
 Step 3: Find out the product of the square of its length to 2(1+√2). This will give the area of the octagon.
 Step 4: By substituting the respective values in the area of an octagon formula 2s^{2}(1+√2) we will get the answer.
 Step 5: Represent the answer in square units.
Solved Examples on Area of Octagon

Example 1: Find the area of the octagon if the length of the side of the octagon is 14 in.
Solution
Length of the side, s = 14 in
Using the formula for the area of the octagon,
A = 2s^{2}(1+√2)
A = 2 ×14^{2}(1+√2)
A = 946.37
Therefore, the area of the octagon is 946.37 square inches.

Example 2: Walter was given an area of an octagon as 25.54 units square. Can you help him find the length of the side of the octagon?
Solution
Area of the octagon, A = 25.54 units square.
Using the formula for the area of the octagon,
A = 2s^{2}(1+√2)
25.54 = 2 × s^{2}(1+√2)
s = 2.3 units
Therefore, the length of the side of the octagon is 2.3 units.
FAQs on Area of Octagon
What Is the General Formula of Area of Octagon?
If the shape is a polygon and it has eight sides, we call it an octagon. To find the area of an octagon we use the following formula. Area of octagon formula = 2 × s^{2} × (1+√2). Where "s" denotes the length of the side of an octagon.
What Is the Area of an Octagon With an Apothem?
Apothem is the line segment drawn perpendicular to the side of the octagon from the center of the octagon. The area of an octagon with an apothem of length l is 8l^{2}(√21).
What Is the Area of an Octagon with a Radius?
The area of an octagon with a radius of length r is 2√2r^{2}. Where "r" is the radius of an octagon.
What Is the Area of an Octagon with Side Length "a"?
The area of an octagon with side length a is 2a^{2}(1+√2). Where "a" denotes the length of the side of an octagon.
What is the Area of an Octagon With Side 5 units?
Area of octagon = 2s^{2}(1+√2)
= 2×5^{2}(1+√2)
= 120.7 units^{2}
Area of the octagon is 120.7 units^{2}.