Math
Diagonal Formula with Problem Solution & Solved Example
Table of Contents
The diagonal formula in mathematics is used to calculate the diagonals of a polygon including rectangles, square, and more similar shapes. When two nonadjacent vertices within a polygon are joined through a single line, it is named as the polygon. Diagonal is formed by joining any two vertices of a polygon except edges. The sloping is also named as the diagonal. Here, we will discuss for diagonal calculation in case of rectangle and the square.
Square is nothing but a regular quadrilateral whose four sides are equal and aligned at the angle of 90 degrees. This is the reason diagonals for a square are also equal. In the case of rectangle, the opposite sides are parallel and they are congruent too. In this case, the diagonals of a rectangle will bisect each other and they are congruent too. Below is give the Diagonal Formula for square and the rectangle.
Diagonal Formula
Diagonal Of Square Formula
\[\LARGE Diagonal\;of\;a\;Square=a\sqrt{2}\]
Where, a is the length of the side of the square
Diagonal Of Rectangle Formula
\[\LARGE Diagonal\;of\;a\;Rectangle=\sqrt{l^{2}+b^{2}}\]
Where,
l is the length of the rectangle.
b is the breadth of the rectangle.
p and q are the diagonals
Diagonal Of A Cube Formula
\[\LARGE Diagonal\;of\;a\;Cube=\sqrt{3}x\]
Where,x is the length of the side of the Cube
Diagonal Of Polygon Formula
Polygon formula to find area:
\[\large Area\;of\;a\;regular\;polygon=\frac{1}{2}n\; sin\left(\frac{360^{\circ}}{n}\right)s^{2}\]
Polygon formula to find interior angles:
\[\large Interior\;angle\;of\;a\;regular\;polygon=\left(n2\right)180^{\circ}\]
Polygon formula to find the triangles:
\[\large Interior\;of\;triangles\;in\;a\;polygon=\left(n2\right)\]
Where, n is the number of sides and S is the length from center to corner.
Diagonal Of Parallelogram Formula
Formula of parallelogram diagonal in terms of sides and cosine $\beta$ (cosine theorem)
\[\LARGE p=d_{1}=\sqrt{a^{2}+b^{2} 2ab\;cos \beta}\]
\[\LARGE q=d_{2}=\sqrt{a^{2}+b^{2}+ 2ab\; cos \beta}\]
Formula of parallelogram diagonal in terms of sides and cosine α (cosine theorem)
\[\LARGE p=d_{1}=\sqrt{a^{2}+b^{2}+2ab\;cos \alpha }\]
\[\LARGE q=d_{2}=\sqrt{a^{2}+b^{2}2ab\;cos\alpha }\]
Formula of parallelogram diagonal in terms of two sides and other diagonal
\[\LARGE p=d_{1}=\sqrt{2a^{2}+2b^{2}d_{2}^{2}}\]
\[\LARGE q=d_{2}=\sqrt{2a^{2}+2b^{2}d_{1}^{2}}\]
To find the total number of diagonals for a polygon with n number of sides, you can use the following formula. This formula is applicable to all shapes that satisfy the properties of a Polygon. No formula in mathematics is written in dreams but there is the logic behind it and the same is true for the belowgiven formula as well. Just memorize it by heart and start solving tough problems in minutes.

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