Area of Regular Octagon Calculator

The regular octagon is defined as the 2 dimensional eight faced geometrical shape, where all the sides are in equal size. The geometrical formula to calculate the area of a regular octagon is mentioned below. Have a look at that and use it for solving questions.

If you know the length of side of a octagon, then

Area of a regular octagon a = 2 (1 + √2) * s².

Here, s is the length of side of a regular pentagon.

If you know perimeter and apothem of regular octagon, then

Regular octagon area = perimeter * apothem.

If you know height, base, then

Area of a regular octagon = 4 * base * height.

The simple and easy step by step manual procedure to figure out the area of a regular octagon is mentioned here. Go through the guidelines and follow them to obtain the area effortlessly.

• Observe the question carefully and measure the length of side of a regular octagon.
• Perform the square of side length.
• And multiply the obtained value by 2 * (1 + √2).
• Final value will be the answer i.e area of a regular octagon.

Example 1: Calculate the area of a regular octagon whose side is 20 cm?

Solution:

Given that,

The length of side of a regular octagon s = 20 cm

Area of a regular octagon a = 2 (1 + √2) * s²

Put the s value in the above formula and simplify

a = 2 (1 + √2) * 20²

= 2 (1 + √2) * 20 * 20

= 800 (1 + √2)

= 1,931.3

∴ Area of a regular octagon is 1931.3 cm².

Example 2: Perimeter of an octagonal stop sign board is 48 cm. Find the area of the signboard?

Solution:

Given that,

Perimeter of an octagonal stop sign board = 48 cm

Perimeter of an regular octagon p = 8 * s

48 = 8 * s

s = 48 / 8

s = 6

The length of side of a octagon s = 6 cm

Regular octagon area a = 2 * s² * (1 + √2)

= 2 * 6² * (1 + √2)

= 2 * 6 * 6 * (1 + √2)

= 72 * (1 + √2)

= 173.82

∴ Area of a regular octagon is 173.82 cm².

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1. What is meant by regular octagon?

A 2 dimensional closed figure having straight line segments. In geometry, octagon is a polygon with 8 sides. If the length of all sides and angles are equal, then it is called regular octagon. The interior angle in regular octagon is 135° and exterior angle is 45°.

2. Define the properties of regular octagon?

• It has eight sides and eight angles of equal length.
• The total number of diagonals in a regular octagon is 20.
• The sum of all interior angles is 1080°, exterior angles is 360°.

3. What is the formula to find the length of diagonal of a regular octagon?

The length of short diagonal d = s * √(2 + √2)

The length of medium diagonal is e = a * (1 + √2)

The length of long diagonal f = s * √(4 + 2√2)

Where, s is the length of the side of an octagon.

4. How to use Area of a Regular Octagon Calculator?

You must enter the side length of a regular octagon in the specified input fields and press on the calculate button to get the exact result that is area of a regular octagon in seconds.