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 diagonalsÂ
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 3Â cm, 5Â cm and angle 45 degrees ?
Solution:
Given a = 3Â cm
b = 5Â cm
angle A = 45°
Formula of diagonal is,
q =
\(\begin{array}{l}\sqrt{a^{2}+b^2-2ab cosA}\end{array} \)
q =Â
\(\begin{array}{l}\sqrt{3^{2} + 5^2 – 2\times 3 \times  5 cos 45}\end{array} \)
q =
\(\begin{array}{l}\sqrt{34 – 30\times 0.707 }\end{array} \)
q = √12.79
=3.576 cm
Diagonal  of parallelogram = 3.576 cm.
simple and good job.