Diagonal of a Parallelogram

A parallelogram's diagonal is the line segment connecting its non-adjacent vertices. A parallelogram has two diagonals, and the length of the diagonals can be calculated using several formulas based on the parameters and dimensions provided.

The diagonals of a parallelogram are drawn by connecting the parallelogram's two non-adjacent vertices. It's worth noting that a parallelogram's two diagonals bisect each other and divide the parallelogram into congruent triangles. You can get all Maths formulas on one-page visit the Maths Formulas section of HT.

Diagonal of a parallelogram formula

The length of the parallelogram’s diagonal is calculated using the formula for parallelogram diagonals. Distinct types of parallelograms have different formulas. For example, examine the diagram below, which depicts a parallelogram and its diagonals. The diagonals are 'p' and 'q,' and the two sides of the parallelogram are 'x' and 'y.'

The length of a parallelogram's diagonals can be calculated using the formula below. Of course, we'll need the lengths of the sides and any known angles for this formula. For example, if we look at the diagram above, we can see that p and q are the diagonal lengths, respectively.

The parallelogram's sides are x and y and angle A and B are two parallelogram interior angles.

Diagonal of a parallelogram

Formula 1: The diagonals of the parallelogram are expressed by the given formula:

P = √(x² + y² − 2xy cosA) = √(x² + y² + 2xy cosB)

q = √x² + y² + 2xy cosA) = √x² + y² − 2xy cosB)

Formula 2: Another formula which expresses the relation between sides of the parallelogram and the length of the diagonals is:

p² + q² = 2(x² + y²)

Where,

p and q are the diagonals, respectively.
x and y are the sides of the parallelogram.

A square, a rectangle, and a rhombus all fall within the category of parallelograms. However, because their qualities differ, the formula for determining their diagonals differs as well.

Diagonal of a Parallelogram