Diagonal of the Parallelogram Formula

The Greek word parallelogrammon gave rise to the word parallelogram, which means bounded by parallel lines. As a result, a parallelogram is a quadrilateral that has parallel lines on opposite sides. 

The opposite sides of a parallelogram will be parallel as well as equal. The line segments that connect the parallelogram’s opposite vertices are referred to as diagonals. A line segment that connects two corners of a polygon that is not an edge is diagonal. However, we can make a diagonal by connecting any two corners (vertices) that are not previously connected by an edge.

Let us take some examples of the Diagonal of the parallelogram formula

1. A parallelogram has sides of 3 cm, 5 cm and an angle of 45 degrees find its diagonal?

Solution:

Given a = 3 cm

b = 5 cm

angle A = 45°

The formula of diagonal is given by

q = √a² + b² – 2abcosA

q = √3² + 5² – 2 x 3 x 5 cos45

q = √34- 30 x 0.707

q = √12.79

    =3.576 cm

Diagonal of parallelogram = 3.576 cm.

2) Find the diagonal of a parallelogram with sides of 2 cm, 6 cm, and an angle of 45°
  Solution:

Given a=2cm,

b=6cm

and ∠A=45°

The formula of diagonal is,

p= √ a²+b²–2abcos(A)

p= √ 2²+6²–2×2×6×cos(45°)

p=√4+36–24×0.707

p= √40–16.968

p= √23.032

p= 4.799cm

Hence, the length of the diagonal of the parallelogram is 4.799cm.

3) Calculate the length of one of the diagonals of a parallelogram of side lengths 4 m and 6 m, if the other diagonal is 8 m.

Solution:

We have,

a = 4

b = 6

x = 8

Using the formula we get,

x²+ y² = 2(a² + b²)

=> 8² + y² = 2 (4² + 6²)

=> 64 + y² = 2 (16 + 36)

=> 64 + y² = 104

=> y² = 40

=> y = 6.32 m