Area of a Regular Octagon Calculator: If you want to find out the area of a regular octagon, then you have arrived at the correct place. Our handy calculator tool computes the regular octagon area easily by taking the length of side of an octagon. By going through this article, you will get a clear cut information on what is the regular octagon, formula to find area of a regular octagon, and simple step by step process to find the area manually.
Formula to Find Area of a Regular Octagon
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.
How to Calculate Regular Octagon Area?
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.
Solved Example Questions
Example 1: Calculate the area of a regular octagon whose side is 20 cm?
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)
∴ 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?
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)
∴ Area of a regular octagon is 173.82 cm².
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FAQ's on Regular Octagon Calculator
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.