## Formula of an Octagon

Among different mathematical branches, geometry is a vital one. In geometry, the students have to read about different shapes and figures and their formulas. Polygon is one of the most important geometrical shapes. The smallest polygon with three sides is called a triangle. The polygon having eight sides is called an octagon. If all the sides of an octagon are equal, that is called the regular octagon. Here, we are going to discuss the area of an octagon formula.

### Formula of Regular Octagon

Here, we are providing the area of regular octagon formula briefly. Assuming all the sides of a regular octagon as ‘a’, the area of octagonal surface formula is 2a2(1+√2). The students can also read the derivation of the area of regular octagon formula. The perimeter of a regular octagon is 8a. The length of the diagonal is a√(4 + 2√2).

### Octagonal Prism Volume Formula

Prism is a geometrical 3D figure. It can have several sides. A prism having eight sides is called an octagonal prism. The area of octagon with apothem is perimeter × apothem / 2, which is also the volume of an octagonal prism.

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### Conclusion

Different problems on the octagon appear in the geometry exam. The students should learn the formula of an octagon correctly so that they can solve problems on an octagon easily. After learning the formulas, they have to memorize them to apply them properly.

Q1. What are the Properties of a Regular Octagon?

Ans: Polygon is one of the most used geometrical shapes. A polygon with 8 sides is called an octagon. If the length of the sides of the octagon is equal, it is a regular octagon. The major properties of a regular octagon are-

All the sides of a regular octagon are equal in length.

A regular octagon has 8 equal interior angles and 8 equal exterior angles.

Each interior angle is 45° and the sum of the interior angles is (45° × 8) = 360°.

Each exterior angle is 135° and the sum of the exterior angles is (135° × 8) = 1080°.

A regular octagon has a total of 20 diagonals.

Q2. Mention the Classifications of the Octagon.

Ans: Octagon is a geometrical shape having eight sides. It has different types depending on different factors. Considering the length of the sides, octagons are of two types- regular and irregular. An octagon having eight equal-length sides is called a regular octagon. If the length of all the sides of the octagon is not equal, it is an irregular octagon. On the other hand, octagons are of two types depending on the pointing of angles- convex and concave octagons. If all the angles of an octagon are pointing towards out, it is called a convex octagon. If any of the angles of an octagon points inwards, it is a concave octagon.

Q3. Mention the Formula of an Octagon in a brief.

Ans: An octagon having eight equal sides is called a regular octagon. There are some particular formulas for the measurement of a regular octagon. If the length of the sides of the regular octagon is a, the area of the octagon is 2a^{2}(1+√2). The perimeter of the regular octagon is equal to the sum of all the sides, which is 8a. By joining the opposite vertices of the regular octagon, we will get the diagonals of the octagon. A regular octagon has 20 diagonals and their lengths are equal. The length of the diagonal of a regular octagon is a√(4 + 2√2). These are the primary measurement formulas of a regular octagon.