Perimeter and Area

Squares and Rectangles

As a kid, the first thing you used to draw while making a house was a rectangle. Do you remember that? The doors and the windows of the house used to be of a rectangular shape. You must have seen the chessboard or a maybe the tiles of your house. Aren’t they of square shape? Do you know how to find the area of a square? Let us study them in detail.

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Perimeter and Area of a Square

Square is a quadrilateral in which all its sides have equal length and all the four corners are right angles.

Area of a Square

  • Perimeter of a Square = 4 × side
  • Area of a Square = side × side

Properties of Squares

  • Opposite sides are parallel, with all sides being equal
  • A square has four lines of symmetry
  • The order of rotational symmetry is 4
  • The diagonals bisect each other at 90° or right angles
  • All sides are equal.
  • Opposite sides are equal and parallel.
  • All angles are equal to 90 degrees
  • The diagonals are equal.
  • Diagonals bisect each other at right angles.
  • Diagonals bisect the angles
  • Any two adjacent angles add up to 180 degrees.
  • Each diagonal divides the square into two congruent isosceles right-angled triangles.
  • The sum of the four exterior angles is 4 right angles.
  • The sum of the four interior angles is 4 right angles.

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Perimeter and Area of a Rectangle

The Above figure is a rectangle. The rectangle is a plane shape with four sides. It is a 4 sided polygon with opposite sides parallel.

Area of a Square

Properties of Rectangle

Area of a Square

                                                                                                                                          ( Source: Quora )

  • Looking at the above figure we see the opposite sides are parallel and equal.
  • This means DA and CB are parallel to one another. What about the other side? If we look at another side we see that those sides are parallel to that means AB and DC are also parallel to one another. So we say that in this figure, the opposite lines are parallel to one another.
  • The sides DA and CB have the same length, so it clear that they are congruent. Also, side DC and AB are congruent to one another. Here in this figure, we have four angles. All the angles in a rectangle are 90°.
  • So we can write it as m∠A = m∠B = m∠C = m∠D = 90°. We can also see that the adjacent angles are supplementary.
  • That is 90° + 90° = 180°. The sum of all the interior angles is 90° + 90°+ 90° + 90° = 360°
  • The diagonals of the rectangle are also congruent to each other and they bisect each other at their point of intersection.
  • A rectangle can also be called as a quadrilateral as it has 4 sides.

Area of a rectangle = l × b

Perimeter of a rectangle = 2 × ( l + b )

Solved Examples For You

Q1. 80 students of the same height stand with both hands stretched all along the sides of’ a rectangular garden, each student covering a length of 1.75 m. Then what is the perimeter of the garden?

  1. 14oom
  2. 140m
  3. 14m
  4. 1400km

Solution: B. Since each student covers the length of 1.75 m

The perimeter of the garden = length covered by 80 students
= 80 × length covered by each student
= 80 × 1.75
= 140m

Q2. Area of a square 625 sqm. Then the measure of its side is

  1. 15m m25m
  2. 20m
  3. 24m

Solution: B. Area of the square = side × side = 625m²
s × s = 25 × 25 = 625²
s = 25m

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