QUADRILATERALQUADRILATERALMathematics (MTH 30104)

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What is Quadrilateral?

• Quadrilateral is define as "A flat shape with four sides".

Quadrilateral means four sides.(Quad means "four" & Lateral means "sides")

Any FOUR-SIDED shape is a Quadrilateral.

But the sides have to be STRAIGHT, and it has to be 2-dimensional (2D).

Properties of Quadrilateral

• FOUR sides (edges)• FOUR vertices (corners)• The INTERIOR ANGLES add up to 360 degrees

For example :

100°+100°+110°+50°=360° 90°+90°90°+90°=360°

Try drawing a quadrilateral, and measure the angles. They should add up to 360°

Types of Quadrilateral

Parallelogram Square

Rectangle

Types of Quadrilateral

Trapezium

Rhombus

Kite

Rectangle

•A rectangle is a four-sided shape where every angle is a right angle (90°).

•Also opposite sides are parallel and equal length.

•It is also a parallelogram.

Rectangle Formula

Area of rectangle : a(base) X b(height)Perimeter of rectangle : 2(a+b)

For example :

5cm

3cm

Find the area of the rectangleArea of rectangle : 5cm X 3cm =15cm²

Find the perimeter of the rectanglePerimeter of rectangle : 2(5cm + 3cm)

= 10cm + 6cm = 16cm

Rhombus

•A rhombus is a four-sided shape where all sides have equal length.

•Also opposite sides are parallel and opposite angles are equal.

•Another interesting thing is that the diagonals (dashed lines in second figure) meet in the middle at a right angle. In other words they "bisect" (cut in half) each other at right angles.

•A rhombus is sometimes called a rhomb, diamonds and it also a special type of parallelogram.

Rhombus FormulaBase Times Height Method : Area of Rhombus = b X h Diagonal Method : Area of Rhombus = ½ X d1 X d2 Trigonometry Method : Area of Rhombus = a² X SinA Perimeter of Rhombus = 4(a) where a = side, b = breadth, h = height, d1, d2 are diagonals

For example :• Given base 3cm height 4cmBTHM : b X h 3cm X 4cm = 12cm²• Given diagonals 2cm and 4cmDM : ½ X d1 X d2 ½ X 2 X 4 = 4cm²• Given side 2cm and angle 90°TM : a² X SinA (2)² X Sin (90°) = 4 X 1 = 4cm²• Given side 2cmPerimeter of Rhombus = 4(2)

= 8cm

Square

• A square has equal sides and every angle is a right angle (90°)

• Also opposite sides are parallel.

• A square also fits the definition of a rectangle (all angles are 90°), and a rhombus (all sides are equal length).

Square FormulaArea of Square = (a)² Perimeter of Square = 4(a) Diagonal of Square = (a)[sqrt(2)]where a = side

For example :

3cm Area of Square = (3cm)² = 9cm²

Perimeter of Square = 4(3cm) = 12cm

Diagonal of Square = (3cm)[sq.root(2)] = 3cm(1.414) = 4.242cm

Parallelogram

• A parallelogram has opposite sides parallel and equal in length.

• Also opposite angles are equal (angles "a" are the same, and angles "b" are the same).

• NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!

Parallelogram Formula

Area of Parallelogram = b (base) X h (height)Perimeter of parallelogram = 2a + 2b

For example :a

b

a

b

Given side a is 3cm side be is 4cm Perimeter of parallelogram : 2(3cm) + 2(4cm)

= 6cm + 8cm = 14cm

b

hGiven the base is 3cm and height is 5cmArea of parallelogram : 3cm X 5cm

= 15cm²

Trapezium

• A trapezium (UK Mathematics) has a pair of opposite sides parallel.

• It is called an Isosceles trapezium if the sides that aren't parallel are equal in length and both angles coming from a parallel side are equal, as shown.

• A trapezoid has no pair of opposite sides parallel.

Trapezium Isosceles Trapezium

Alternate Anglea

b

• Trapezium is a special quadrilateral because it has a pair of parallel line.

• If the trapezium has no parallel line, the alternate angles would not be formed.

• ∠ a = b∠ , "Z" shape is formed.

• ∠ABC + BCD = 180°∠ (The parallel angles match together and it will formed a 180°)

A B

CD

Trapezium Formula Area of Trapezium = ½ X (a + b) X h where a, b = sides, h = height

Perimeter of Trapezium = a + b + c + d where a, b, c, d = sides

For example :• Find the area of trapezium. Given length b is 3cm and length a is 4cm and height is 2cm.Area of Trapezium = ½ X (4 + 3) X 2

= ½ X 14 = 7cm²

• Given side a is 3, b is 4, c is 5 and d is 6Perimeter of Trapezium = 3 + 4 + 5 + 6

= 18cm

Kite

• A kite has two pairs of sides.

• Each pair is made up of adjacent sides that are equal in length.

• The angles are equal where the pairs meet.

• Diagonals (dashed lines) meet at a right angle

• The diagonals of a kite are perpendicular.

Kite Formula Diagonal Method : Area of Kite = ½ X d1 X d2 Trigonometry Method: Area of Kite = a X b X SinCPerimeter of Kite = 2 (a + b) where a = length, b = breadth, d1, d2 are diagonals

For example :• Find the area of kite given diagonals 2cm and 4cmDM : Area of kite = ½ X 2 X 4

= 4cm²

• Given length 2cm and breadth 3cm. Find the area.TM : Area of kite = 2 X 3 X Sin 90°

= 6cm²

• Given length 2cm and breadth 3cm. Find the perimeter.Perimeter of kite = 2 (2cm + 3cm)

= 10cm

Complex QuadrilateralsWhen two sides cross over, you call it a "Complex" or

"Self-Intersecting".

For example :

• They still have 4 sides, but two sides cross over.

Thank You Very Much !

That's all for Quadrilaterals