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A Quadrilateral is a closed figure with four sides, four corners and four vertices and the sum of the interior angles is 360°.

In the above figure, ABCD is a quadrilateral with four sides AB,BC, CD and DA, and the four angles $\angle$A, $\angle$B, $\angle$C and $\angle$D formed by the four vertices A,B,C and D.

Some of the examples of quadrilaterals are classroom board, a book, table etc.

In a parallelogram,

- The opposite sides are parallel to each other.
- Opposite sides are congruent.
- Opposite angles are congruent.
- The diagonals of a parallelogram bisect each other.
- Any pair of consecutive angles are supplementary (their sum is 180 degrees).

In a rectangle,

- The opposite sides are parallel to each other.
- Opposite sides are congruent.
- Opposite angles are congruent.
- The diagonals bisect each other.
- All the angles are right angles.
- The diagonals are congruent.

- Two disjoint pairs of consecutive sides are congruent.
- The diagonals are perpendicular to each other.
- One diagonal is the perpendicular bisector of the other diagonal.
- One of the diagonals bisects a pair of opposite angles.
- One pair of opposite angles are congruent.

In a Rhombus,

- The opposite sides are parallel to each other.
- The diagonals of a parallelogram bisect each other.
- Two consecutive sides are congruent by definition.
- All sides are congruent.
- All the four sides are right angles.
- The diagonals are perpendicular bisectors of each other.
- The diagonal divides the Rhombus into four congruent right triangles.

In a Square,

- The opposite sides are parallel to each other.
- Opposite sides are congruent.
- Opposite angles are congruent.
- The diagonals bisect each other.
- The diagonals are congruent.
- All sides are congruent.
- All the four angles are right angles.
- The diagonals are perpendicular bisectors of each other.
- The diagonals form four isosceles right triangles.

In an Isosceles Trapezoid,

- The legs are of an Isosceles trapezoid are congruent.
- The bases are parallel to each other.
- The lower base and upper base angles are congruent.
- The diagonals are congruent.
- Any lower base angle is supplementary to any of the upper base angles.

- Parallelogram
- Rectangle
- Kite
- Rhombus
- Square
- Isosceles Trapezoid

Rectangles, Rhombuses and Squares all different types of Parallelograms.

Solution:

Area of a parallelogram = base $\times$ height

= 14 $\times$ 6

= 84 sq cm

A = l . w

Solution:

Area of a rectangle = length $\times$ width

= 11 $\times$ 8

= 88 sq m

If the diagonals are given as d

Area of a Kite =$\frac{1}{2}$ (d

Area of a kite =$\frac{1}{2}$ (product of the diagonals)

= $\frac{1}{2}$ ( d

= $\frac{1}{2}$ ( 26 $\times$ 18)

= 234 sq cm

If the diagonals are given as d

Area of a Rhombus = $\frac{1}{2}$ (d

Solution:

Area of a Rhombus =$\frac{1}{2}$ (product of the diagonals)

= $\frac{1}{2}$ ( x $\times$ y)

= $\frac{1}{2}$ (18 $\times$ 10)

= 90 sq cm

Solution :

Area of a square = side $\times$ side

= 8 $\times$ 8

= 64 sq cm

6. Area of a Trapezoid (Trapezium)

(a and b are the lengths and h is the height)

Solution:

Area of a Trapezoid = $\frac{1}{2}$ (a+b).h

= $\frac{1}{2}$ (9 + 14). 6

= 69 sq inches.

In the figure above, ABCD is a cyclic quadrilateral inscribed in a circle with centre O

A quadrilateral is said to be cyclic quadrilateral if there is a circle passing through all its vertices

Sum of the opposite angles of a cyclic quadrilateral is 180°

A = b.h

2. Area of a Rectangle =

A = l . w

If the diagonals are given as d

Area of a Kite = $\frac{1}{2}$ (d

If the diagonals are given as d

Area of a Rhombus = $\frac{1}{2}$ (d1 $\times$ d

5.

6.