AREA AND PERIMETER OF A SQUARE – MindSpark.

What is a square?

A square is a quadrilateral ( a shape having four sides) having equal sides and angles(90°each).

Perimeter of Square

Perimeter means the length of the boundary of a shape, so in a square, the perimeter will be the sum of all the sides. 

Perimeter of a square = a + a + a + a = 4 × a = 4a , where ‘a’ is the side of the square. 

Therefore the perimeter of a square is   4 × (side of the square).

Area of Square

The area of a square means the measure of the surface covered by the square, which is equal to the product of its two sides.

Area of square =a \times a=a^{2}

Example

1. Find the area and perimeter of a square whose side is 11 cm.

Solution:

Area of square =a \times a=a^{2}.

Here side of the square is 11 cm,

therefore area of square =11 \times 11=11^{2}=121 \mathrm{~cm}^{2}

The perimeter of a square = 4 x side = 4 x 11 = 44 cm 

2. If the area of a square is 400 \mathrm{~cm}^{2}, then find the side of the square and the perimeter of the square.

Solution:

Area of square =a \times a=a^{2}. It is given that the area of the square is 400 \mathrm{~cm}^{2}. Therefore side of the square is 

   400=a \times a=a^{2}
⇒ 400=a^{2}

We get a = 20 cm .

Therefore the side of the square is 20 cm.

Now we’ll find the perimeter of the square 

Perimeter of a square = 4 x side = 4 x 20 = 80 cm.