You can find out the diagonals of the polygon by using the polygon formula. But before finding the number of diagonals, let’s try to understand some terms and define them to grasp the concept easily.

So, let’s learn how to find the **diagonal of a Polygon Formula**.

**What is diagonal?**

A diagonal is a straight line or line segment which connects the opposite corners of the polygon through the vertices. Now to understand the diagonal, we should know the terms polygon and vertex.

**Polygon**is a 2-dimensional geometric figure and is made up of straight-line segments and not curves. It should have a closed figure, so two straight lines cannot form a closed figure which means that a minimum of three straight line segments is required to connect end to end to form a closed figure.- The polygon, which has a minimum of 3 sides, is a
**triangle**, also known as 3-gon. **Vertex**is the corner of the shape or a point where two line segments meet.

You can understand that a diagonal is a line segment that connects two non-adjacent vertices of a polygon. Here, one thing to remember is that the line segment which connects two adjacent sides is not counted as a diagonal. And there is no diagonal from a vertex back to itself, which means that there are three fewer diagonals than the number of vertices.

**Polygon formula **

- The number of diagonals from a single vertex is three less than the number of vertices or sides, which is =
**(n-3)** - There are a total N number of sides for a polygon, which results in n (n-3) diagonals.
- Each diagonal has two ends that count twice, so we need to divide them by 2.

Therefore, the formula for counting diagonals of the polygon** **is: n (n-3)/2

Additionally, there are various polygons divided based on the sides and angles of a polygon, namely:

- Regular polygon- total number of sides and measure of interior angles are equal
- Irregular polygon- total number of sides and measure of interior angles are different and not equal
- Concave polygon- interior angles are strictly less than 180 degrees
- Convex polygon- one or more interior angles of a polygon are more than 180 degrees.

**Finding the number of diagonals **

Since the polygon has a finite number of sides, we can call it an n-polygon. Here ‘n’ means a number of sides or vertices. Now let’s find out the number of diagonals for n-polygon with solved easy examples and FAQS. And let’s take the examples for ‘n’ up to 8 vertices or sides.

- Let n = 3, which is a
**triangle.**But in triangles, there are only adjacent vertices and no non-adjacent vertices. So the number of diagonals in the triangle is zero. - Let n = 4, which is
**quadrilateral.**By the polygon formula n (n-3)/2

= 4 (4-3)/2

= 2

Therefore, the number of diagonals in the quadrilateral is 2.

- Let n = 5, which is
**a pentagon**; with the help of the polygon formula, the number of diagonal pentagons has 5.

- Let n = 6, which is
**a hexagon**; the number of diagonals in a polygon hexagon is 9. - Let n = 7, which is
**heptagon**; - Let n = 8,
**an octagon**;

**Finding the number of diagonals in some special cases**

Let’s find out the polygon formula in the case of **square, rectangle, and cube.**

- In the case of a square, the formula for finding a number of diagonals is a with two under root,
- In the case of a rectangle, the formula for finding the number of diagonals is root under L square + B square,
- In the case of a cube, the formula for finding the number of diagonals is and here’s the side of the cube.

For even more insights on polygons, you can refer diagonal of the polygon formula and can practice some problems to challenge your conceptual understanding.

**Conclusion**

You now know the conceptual and practical areas in the polygon formula for finding the number of diagonals for different types of polygons. With a simple formula, n (n-3)/2,** **you can find both numbers of diagonals and the number of sides or vertices under five minutes. Even when information about one area is given, you can quickly find the answer using the discussed formula.

**Frequently Asked Questions **

**What are adjacent and non-adjacent sides?**

Adjacent sides mean they have a common endpoint or border, and the non-adjacent sides’ means simply not having a common endpoint or border.

**How to quickly use the polygon formula for finding diagonals in nonagon?**

Nonagon means the polygon which has 9 sides. So the polygon formula is n (n-3)/2, which is-

9 (9-3)/2 = 27 diagonals.

**Which type of polygon has equal diagonals?**

Rhombus with four equal sides, which is also a parallelogram, has equal diagonals.

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