# Diagonal Formula

## Diagonal Formula

Geometry involves a thorough examination of shapes and structures to ascertain their characteristics and other pertinent details. The study of all shapes is covered in this discipline, which also provides precise formulas to determine the properties of any shape as needed.

A diagonal is a slanted line segment that joins any two vertices of a given polygon found on two different edges or sides. These lines, whether straight or angled, connect two corners of a square, rectangle, rhombus, or another shape.

In order to determine how many and how long diagonals are present in a polygon, one can use the Diagonal Formula. The Diagonal Formula can be understood by referring to the Extramarks website or mobile application.

### What Is Diagonals Formula?

Any line segment that joins two shape vertices that are not previously connected by an edge is referred to as a Diagonal Formula. Not in a straight line-up, down, or across. The diagonals are always in the form of a straight line. To put it another way, a diagonal is a line that, at its vertex, joins the opposite corners of a polygon or a polyhedron.

The Diagonal Formula is always located inside the interior of convex polygons. Think of a rectangular door. Students can draw a line from the bottom opposite corner to the top hinge corner. Another option is to draw a straight line from the bottom hinge corner to the top opposite corner. Those two will be potential diagonals.

Simple concave polygons may have diagonals that cross sides and partially lie outside the polygon’s interior. Still, they are diagonals. Examples of concave polygons with diagonals outside their shapes are darts and stars.

### Formula for Diagonals

In order to determine how many and how long diagonals are present in a polygon, one can use the Diagonal Formula. The formula for determining how many diagonal lines there are in an n-sided polygon is as follows:

n-sided polygon = n(n – 3)/2

Where,

n is the number of sides of the polygon

There are various Diagonal Formula in geometry for the various types of polygons that are covered. These calculations are utilised only for that specific polygon. These polygons’ formulas are provided.

### Diagonal of a Square

In order to determine the length of a diagonal, let’s now examine a few different Diagonal Formula.

Diagonal of square = a√2

Where

a is the length of the side of the square.

### Diagonal of a Rectangle

For rectangles, l stands for the rectangle’s length and b for its height.

Diagonal of a Rectangle = √l2 + b2

### Diagonal of a Parallelogram

If one diagonal’s length is known, the formula for the other diagonal is:

p2 + q2=2(a2 + b2)

Where

a and b are the sides of the parallelogram

p and q are the two diagonals of the parallelogram

### Examples Using Diagonals Formula

Example 1: Sam is walking around a rectangular park whose length of 10m and breadth is 8m. Find out the diagonal of a rectangular park where Sam is walking.

Solution:

To find The diagonal of a rectangular park.

Given parameters are,

Length = 100m

Using the Formula for Diagonals,

Rectangle Diagonal = √[l2 + b2]

= √[102 + 82 ]

= √

= 12.80 m

Answer:  The diagonal of a rectangular park where Sam is walking is 12.80 m.

Example 2: The area of the rhombus is 100 inch2. Determine the second diagonal of a rhombus whose one of its diagonal one measures 10 inches.

Solution:

To find: The second diagonal of a rhombus

Given parameters are,

The area of the rhombus = 100 inch2

Using the Diagonal Formula,

Diagonal of a Rhombus, p = 2(A)/q and q = 2(A)/p

p = 2(100)/10

p = 20 inches.

Example 3: Determine the length of the diagonal of a square whose side measure is 5 units

Solution:

To find: The diagonal of a square

Given parameters are,

Side of square = 5 units

Using the Formula for Diagonals,

Square Diagonal = a√2

= 5√2

= 7.07 units

Answer:  The diagonal of a square is 7.07 units.