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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. This shape is an eight-sided polygon consisting of eight interior and exterior angles. The area of the octagon can be calculated by diving it into 8 equal isosceles triangles. In this mini-lesson, we will discuss the octagon area formula in detail.

1.	What is the Area of Octagon?
2.	Area of Octagon Formula
3.	How to Calculate Area of Octagon?
4.	FAQs on Area of Octagon

What is the Area of Octagon?

An octagon is a 2-dimensional shape with 8 sides and the area is the space within the 8 sides of the shape. To calculate the area of the octagon we can use the area of an isosceles triangle. We divide the area of the shape into eight equal isosceles triangles and calculate it accordingly. A regular octagon has the length of the sides equal and the angles between these sides are equal. The measure of each interior angle is 135° and the exterior angles measure 45° each.

Area of Octagon Formula

The formula used to calculate the area of an octagon is:

2s²(1+√2), where s is the length of the side of the octagon.

Area of Octagon

How to Calculate Area of Octagon?

The area of an octagon is 2s²(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 2s²(1+√2) we will get the answer.
Step 5: Represent the answer in square units.

☛Related Topics

Listed below are a few topics that are related to the area of an octagon.

Area of Octagon Examples

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 = 2s²(1+√2)

A = 2 ×14²(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 = 2s²(1+√2)

25.54 = 2 × s²(1+√2)

s = 2.3 units

Therefore, the length of the side of the octagon is 2.3 units.
Example 3: Find the area of a regular octagon if its side measures 5 units.

Solution:

The sides of a regular octagon are of equal length. Here, the side length, a = 5 units. We can find the area of the octagon using the formula, Area of a Regular Octagon = 2a²(1 + √2). Substituting the value of 'a' in the formula, we get, Area of a Regular Octagon = 2a²(1 + √2) = 2 × (5)² × (1 + √2) = 50 × (1 + √2) = 120.71 square units. Therefore, the area of the octagon is 120.71 square units.

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Practice Questions on Area of Octagon

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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 × s² × (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 8l²(√2-1).

What is the Area of an Octagon with a Radius?

The area of an octagon with a radius of length r is 2√2r². 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 2a²(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 = 2s²(1+√2)
= 2×5²(1+√2)
= 120.7 units²
Area of the octagon is 120.7 units².

How to Find the Area of an Octagon?

The area of an octagon is calculated with the formula, 2a²(1 + √2); where 'a' is any one side length of the octagon. It is expressed in square units like inches², cm², and so on. In the case of an irregular octagon, there is no specific formula to find its area. We divide the octagon into smaller figures like triangles. Then, after calculating the area of all the triangles, we add their areas to get the area of the octagon.

What is an Octagon in Geometry?

Octagon is an eight-sided two-dimensional geometrical figure which consists of 8 interior angles and 8 exterior angles. The name 'octagon' is derived from the Greek word 'oktágōnon' which means eight angles.

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