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

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

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

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

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 =

\begin{array}{l} \sqrt{a^{2} + b^{2} - 2 a b c o s A} \end{array}

q =

\begin{array}{l} \sqrt{3^{2} + 5^{2} - 2 \times 3 \times 5 c o s 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.

FORMULAS Related Links
Surface Area Of A Sphere Formula	Area Of Quadrilateral General Formula
Sphere Formula	Area Of A Segment Of A Circle
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Dot Product Formula	Tangential Acceleration Formula
Weighted Average Formula Example	Sample Variance Formula

FORMULAS Related Links

Surface Area Of A Sphere Formula

Area Of Quadrilateral General Formula

Sphere Formula

Area Of A Segment Of A Circle

Basic Calculus Formulas

Air Pressure Formula

Dot Product Formula

Tangential Acceleration Formula

Weighted Average Formula Example

Sample Variance Formula

Diagonal of Parallelogram Formula

Diagonal of Parallelogram Formula

Solved Examples

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