## Area of SquareA square is a closed figure on a 2D plane that has four parallel sides. The property of the square is that all the sides (breadth and length) must have equal length. In a square, each angle is of 90�. In this section, we will learn area of square formula, and how to find area of a square. ## Area of SquareThe area is the region covered by the four-sides. In other words, the number of square units it takes to fill a square completely. In the following image, we have divided a square into five rows and five columns. It makes the multiple small squares that completely fills the square. Hence 25 small squares represent the area of the square. ## Area of Square FormulaTo calculate the area of a square, multiply the base to itself. In short, the square of the side is the area of the square. Where a is the side of a square whose length is a. ## When the diagonal is givenWe can also calculate the area of a square if the length of the diagonal is given. The area is half the product of the diagonals. Both the diagonals are equal length. Where d is the length of either diagonal. ## DerivationConsider a square as a rectangular shape whose length is l and breadth are b. According to the area of rectangle formula: A = l*bWhere, - A is the area
- l is length
- b is breadth
Suppose that a side of a square is a. Then the area of the square will be: A = a*b We know that all sides of the square are equal length. Then, A = a*a
## Examples
We have given that a side of the square is 12 cm. We know that
A = 12
Given, perimeter (P) = 24 yd We know that
Where a is the length of the side. Putting the value of P in the above formula we get: 24 = 4a a = 24/4 a = 6 yd We know that,
Substitute value and simplify, we get: A = 6*6 = 36 yd
Given, length of diagonal (d) = 6 m We know that,
Putting the value of d in the above formula, we get: A = (6) A = 36/2 A = 18 m
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