Now, in this blog, we will study the perimeter and area of squares. Let us find the perimeter and area of a square.
To find the area we take a square of side a whose length and breadth are equal. Now, take a strip of length a, which can be moved from side AB to CD. In this process, this strip covered an area of an into a. So, the area of the square of side a is equal to (a square) that is; side square.
Now, the perimeter of a square is the distance around the outside of the square. A square has four sides of equal length. The formula for finding the perimeter of a square is 4 into (Length of a Side).
Area of Square
Let the side of the square be a.
Area of the square = a x a = a2 = (side)2
Perimeter of the square = a + a + a + a = 4 x a = 4 x side
Examples
Example: Find the area and perimeter of the squares given in the figure.
Solution: In the figure, the side of square ABCD = 1 cm
Area of square ABCD = (AB)2 = (1)2 = 1 cm2
Perimeter of square ABCD = 4(AB) = 4(1) = 4 cm
Area of square PQRS = (PQ)2 = (3)2 = 9 cm2
Perimeter of square PQRS = 4(PQ) = 4(3) = 12 cm
Read More: Euclid Geometry Class 9: Introduction To Euclid's Geometry - Math
Frequently Asked Questions (FAQs)
If you know the length of the diagonal of the square, you can calculate the area using the formula: Area = diagonal 2 2 Area= 2 diagonal 2 .
Sure! If a square has a side length of 5 units, its area would be 5 × 5 = 25 5×5=25 square units.
Understanding the area of a square is important in various fields such as architecture, engineering, and everyday tasks like home improvement projects, where you need to measure and manage space efficiently.
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