Examples of Diagonals Formula

Example 1: Find the length of the diagonals of a square whose side measures 10cm.

Solution:

Given,

Length of Side of Sqaure = 10 cm

Diagonal of Square = a√(2)

⇒ Diagonal of Square = 10√(2)

⇒ Diagonal of Square = 14.14 cm

Thus, the length of diagonal of square is 14.14 cm.

Example 2: Find the second diagonal of a rhombus having its first diagonal measuring 20 cm and the area of the rhombus is 200 cm² 

Solution:

Given,

Let two diagonals be p and q

Length of diagonal p = 20 cm

Area of Rhombus = 200 cm²

q = 2(A)/p

⇒ q = 2 × 200/20

⇒ q = 400/20

⇒ q =  20 cm

Thus, the other diagonal of the Rhombus is 20 cm.

Example 3: Find the first diagonal of a rhombus having its second diagonal measuring 5cm and the area of the rhombus is 100cm².

Solution:

Given,

Let two diagonals be p and q

Length of One diagonal q = 5 cm

Area of Rhombus = 100 cm²

p = 2(A)/q

⇒ p = 2 × 100/5

⇒ p = 200/5

⇒ p = 40 cm

Thus, the other diagonal of the Rhombus is 40 cm.

Example 4: Find out the diagonal length of a rectangle having its length 20cm and breadth of 12cm.

Solution:

Given,

• Length of Rectangle = 10 cm
• Breadth of Rectangle = 3 cm

We have,

Diagonal of Rectangle = √(l² + b²)

⇒ Diagonal of Rectangle = √(20)² + (12)²

⇒ Diagonal of Rectangle =√(400+144)

⇒ Diagonal of Rectangle =√(544)

⇒ Diagonal of Rectangle = 23.32 cm

The length of diagonal of recatngle is 23.32 cm

Diagonal Formula is the formula that is used to calculate the length of the diagonal of any polygon. A diagonal is a slant line that joints two alternate sides of any polygon and finding its length is very important for solving various problems of geometry.

There are different ways for finding the diagonal of any polygon and we use various techniques for that purpose. Using Pythagoras Theorem is one such way. We have to study the Diagonal Formula in Class 8. In this article, we will learn about the Diagonal definition, its formula, various examples, and others related to it.