# Diagonal of Parallelogram Formula

A parallelogram is a quadrilateral whose opposite sides are parallel and equal. The opposite sides being parallel and equal, forms equal angles on the opposite sides. Diagonals of a parallelogram are the segments which connect the opposite corners of the figure.

Where,
p,q are the diagonals

a,b are the parallel sides

$\LARGE p=\sqrt{a^{2}+b^{2}-2ab\cos (A)}=\sqrt{a^{2}+b^{2}+2ab\cos (B)}$

$\LARGE q=\sqrt{a^{2}+b^{2}-2ab\cos (A)}=\sqrt{a^{2}+b^{2}-2ab\cos (B)}$

$\LARGE p^{2}+q^{2}=2(a^{2}+b^{2})$

### Solved Examples

Question 1:

Find the diagonal of a parallelogram with sides 3 cm, 5 cm and angle 45 degrees ?

Solution:

Given a = 3 cm
b = 5 cm
angle A = 45°
Formula of diagonal is,
q = $\sqrt{a^{2}+b^2-2ab cosA}$

q = $\sqrt{3^{2} + 5^2 – 2\times 3 \times 5 cos 45}$

q = $\sqrt{34 – 30\times 0.525}$
q = 4.27 cm
Diagonal  of parallelogram = 4.27 cm