Diagonal of Square

In Geometry, the diagonal of square is a line segment that connects two vertices that are not adjacent to each other along an edge of the square. Informally, any sloped line is referred to as a diagonal. Learn the definition, derivation and diagonal of a square formula, along with numerous worked-out examples, in this article.

Table of Contents

• Definition
• Formula
• Derivation
• Examples
• FAQs

What Is the Diagonal of Square?

A square contains two diagonals, which are created by connecting the square’s opposing vertices. In order to relate the properties of the diagonal of a square, consider the square, which is given below.

• A square’s diagonals are of equal length.
• They are each other’s perpendicular bisectors.
• The diagonal divides the square into two identical isosceles right-angled triangles.

Also, read:

• Area of Square
• Perimeter of Square

Diagonal of Square Formula

As we know, the diagonal of a square divides the square into two congruent isosceles right triangles. Hence, by using the Pythagoras theorem, we can easily derive the formula for the diagonal of a square.

The formula for the diagonal of a square is:

Diagonal of a square, d = a√2 units

Where,

“d” is the diagonal of a square.

“a” is the side length of a square.

Also, check out: Diagonal of Square Formula

Diagonal of Square Derivation

Consider a square ABCD, as shown in the figure. As the square’s diagonal divides the square into two congruent isosceles right triangles, let us consider the triangle ADC.

Now, by using the Pythagoras theorem, we can find the length of the diagonal of a square, which is the hypotenuse of a triangle (d).

If “a” is the side length of a square, then the hypotenuse (diagonal of a square) can be found as follows:

d² = a² + a²

d² = 2a²

Taking the square root on both sides, we get

d = a√2 units

Hence, the diagonal of square is a√2 units.

Also, check: Diagonal of Square Calculator

Diagonal of Square Examples

Example 1:

Find the diagonal of a square whose side is 10 cm.

Solution:

Given that, the side length of a square, a = 10 cm.

As we know, the formula to find the diagonal of a square is a√2 units.

Now, substitute the value of “a” in the formula, and we get

Diagonal of square, d = 10√2 units.

d = 10(1.414) [since, √2= 1.414]

d = 14.14 cm

Therefore, the diagonal of a square whose side equals 10 cm is 14.14 cm.

Example 2:

What is the diagonal of a square plate whose side is 28 cm?

Solution:

Given, the side length of a square plate, a = 28 cm.

We know that the diagonal of the square formula is d = a√2 units.

Substituting the value of “a” in the formula, we get

Diagonal of a square plate, d = 28×√2

d = 28 × 1.414

d = 39.59 cm

Hence, the diagonal of a square plate is 39.59 cm.

Example 3:

Find the diagonal of a square length whose area is 16900 m².

Solution:

Given that the area of a square = 16900 m²

We know that the area of a square is a² square units.

Hence, a² = 16900

Now, take the square root on both sides; we get

√a² = √(16900)

Hence, the side length of a square, a = 130 m.

Now, substitute the value of “a” in the diagonal of the square formula.

Diagonal of a square, d = a√2 units

d = 130 × √2

d = 130 × 1.414

d = 183.8 (approximately)

Therefore, the diagonal of a square, whose area is 16900m², is approximately equal to 183.8 m.