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.

 Diagonal of a Parallelogram

Where,
p,q are the diagonals 

a,b are the parallel sides

[LARGE p=sqrt{a^{2}+b^{2}-2abcos (A)}=sqrt{a^{2}+b^{2}+2abcos (B)}]

[LARGE q=sqrt{a^{2}+b^{2}+2abcos (A)}=sqrt{a^{2}+b^{2}-2abcos (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 = $sqrt{3^{2} + 5^2 – 2times 3 times  5 cos 45}$

q = $sqrt{34 – 30times 0.707 }$

q = √12.79

=3.576 cm

Diagonal  of parallelogram = 3.576 cm.

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