Diagonals Formula Definition, Use & Solved Examples

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Diagonals Formula

A diagonal is a slanted or sloping line that links two polygon vertices that are not on the same edge. The word diagonal comes from the Greek word "diagnosis," which means "to go from one angle to another." Let's look at the formulas for diagonals for various polygons such as squares, rectangles, rhombuses, and parallelograms.

What Is Diagonals Formula?

The diagonal formula is a formula for determining the number of diagonals and their lengths in various polygons. An n-sided polygon has n(n-3)/2 diagonal lines, where n is the number of sides.

Let's look at the formulas for the diagonals of various polygons. You can get all Maths formulas on one-page visit the Maths Formulas section of HT.

Diagonals' Formula:

The formulas for different polygons' diagonals are as follows:

Square Diagonal Formula:

Square Diagonal: a√2

where ‘a is the length of a square's side

Rectangle Diagonal Formula:

Rectangle Diagonal: $\sqrt{[l^{2} + b^{2}]}$

Where l is the rectangle's length, and The width of the rectangle is b.

Rhombus Diagonal Formula:

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

Where A is the rhombus's area and p and q are the rhombus's two diagonals.

Parallelogram Diagonal Formula:

Parallelogram Diagonals:

$p = \sqrt{x^{2} + y^{2} - 2 x y \cos A} = \sqrt{x^{2} + y^{2} + 2 x y \cos B} a n d q = \sqrt{x^{2} + y^{2} + 2 x y \cos A} = \sqrt{x^{2} + y^{2} - 2 x y \cos B}$

Also, p² + q²= 2 (a²+ b²)

Where x and y are the parallelogram's sides, and p and q are the parallelogram's two diagonals.

Solved example of Diagonals Formula

Example: Sam is strolling across a rectangular park with a length of 10 metres and a width of 8 metres. Determine the diagonal of the rectangular park in which Sam is walking.

Sol: To find the diagonal of a rectangular park.

Given parameters are,

Length = 100m

Breadth = 91m

Using Formula for Diagonals,

Rectangle Diagonal: √[l² + b²]

= √[10² + 8²]

= √164

= 12.80 m

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

Diagonals Formula