Diagonal Of Square Formula

Diagonal Of A Square Formula

Any slanted line that cuts through the opposing angles of a figure is said to be diagonal. The Diagonal Of Square Formula is important for finding out the length of a square. It connects two corners of a polygon, square, rectangle, cube, or cuboid. To determine the diagonal length of various figures in relation to their sides, a diagonal formula is used. Additionally, the square’s diagonal always forms a 45-degree angle. In addition, a square’s diagonal is equal to the square root of twice the side’s square. Simply put, the square root of two, or 1.414, multiplies the length of a side to get the length of a diagonal.

A square is regarded as a regular quadrilateral because it has four equal sides and four equal angles. Right angles are those that are shared by a square’s adjacent sides. In addition, the square’s diagonals are equal and split at a 90° angle. The parallelogram with two adjacent equal sides and one right vertex angle is known as a square. Additionally, a square, which has an equal length and width, can be seen as a special case of a rectangle. The space a square takes up is its area. Chessboards and square wall clocks are a few examples of square shapes. To determine the area that these objects occupy, we can use the square’s area formula.

What is the Diagonal of a Square?

A line segment that connects any two non-adjacent vertices forms a square’s diagonal. Two equal-length diagonals that cut across each other at right angles make up a square. When a square’s side length is known, the diagonal of the square can be calculated using the Diagonal of Square Formula. A square is a closed figure with four sides that are all the same length, and its interior angles are all 90 degrees. A square can have many different characteristics. The following list includes some of a square’s key characteristics.

1. A quadrilateral with four sides and four vertices is called a square.
2. The square’s four sides are equal to one another.
3. A square’s diagonals are parallel to one another.
4. Each vertex of a square has a 90° interior angle.
5. 360° is the total of all interior angles.
6. A square’s diagonals are 90 degrees apart from one another.
7. The diagonals are all the same length.
8. A square is also referred to as a parallelogram because its sides are parallel.

What is the Diagonal of Square Formula?

Diagonal lines are lines that cut through opposing angles of a figure. In order to determine the length of a square, the Diagonal Of Square Formula is necessary. It is used to connect the corners of a polygon, square, rectangle, cube, or cuboid. A diagonal formula is used to determine the diagonal length of various figures in relation to their sides.

Derivation of Diagonal of Square Formula

In a square, both diagonals are the same length. The Pythagoras theorem is used to determine the length of the diagonal d of a square with side length x. See how the letter d indicates the diagonal length in the following square and the letter x indicates the side length. It is necessary to understand how the equation for determining a square’s diagonal was derived. 

A square is divided into two equal triangles by its diagonal. If one of the triangles is denoted by PQR. Looking at the square’s PQR triangle. Since it is known that a square’s angles are all 90 degrees, the Pythagoras theorem can be used to determine the hypotenuse, which in this instance is taken as d. According to the Pythagoras theorem, the square of the hypotenuse side in a right-angled triangle equals the sum of the squares of the other two sides.

Currently, 

d2=x2+x2 

Which can also be written as d2=2x2 

And d = square root of 2x2

is written as d= √2x

As a result, d=√2x is the Diagonal Of Square Formula.

Diagonal of a Square Formula

Diagonal Of Square Formula is helpful in finding the diagonal of a square. The Pythagoras theorem plays an important role in deriving the Diagonal Of Square Formula. Students can also find out the length of the side of a square by using the Diagonal Of Square Formula.

Examples Using Diagonal of Square Formula

It is important to practice questions to learn the correct implementation of the Diagonal Of Square Formula. Students who are finding it difficult to practice questions based on the Diagonal Of Square Formula can take assistance from the Extramarks learning platform. All the difficult questions regarding the Diagonal Of Square Formula can be solved with the assistance of NCERT solutions available on Extramarks. Students can also download NCERT solutions for other Mathematics topics from Extramarks.

Practice Questions on Diagonal of Square

Practising questions on a regular basis helps students in scoring well in the Mathematics examination. A particular topic in Mathematics can be mastered by practising questions from time to time. It is important to practice questions based on the diagonal of a square topic. Practising questions consistently will also boost the confidence of students for the Mathematics examination. Some questions can be challenging to solve for students. They need assistance from expert teachers who can guide them well. The teachers at Extramarks can help students in getting a proper solutions to questions.