quadrilateral class 9.pptx

Quadrilateral and its types

1. QUADRI L A T E RAL Prepared by: SHARDA CHAUHAN TGT MATHEMATICS CLASS 9

2. 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) .

3. Prope r ties of Q u a d r ilat e ral 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°

4. Types of Quadrilateral P a r a ll e l o gram S q ua r e R e c t a ng le

5. Types of Quadrilateral T rape z i um R h o m bu s Kite

6. R e cta n gle 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 .

7. Rectangle Formula Area of rectangle : a(base) X b(height) Perimeter of rectangle : 2(a+b) For example : 5cm 3 cm Find the area of the rectangle Area of rectangle : 5cm X 3cm =15cm² Find the perimeter of the rectangle Perimeter of rectangle : 2(5cm + 3cm) = 10cm + 6cm = 16cm

8. 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 .

9. Rhombus Formula Base 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 4cm BTHM : b X h 3cm X 4cm = 12cm² Given diagonals 2cm and 4cm DM : 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 2cm Perimeter of Rhombus = 4(2) = 8cm

10. 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 ).

11. Square Formula Area 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

12. 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 !

13. 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 h Given the base is 3cm and height is 5cm Area of parallelogram : 3cm X 5cm = 15cm²

14. T ra p e z i u m 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

15. Alternate Angle 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 " s h a pe i s for m e d. ∠ ABC + ∠ BCD = 180° (The parallel angles match together and it will formed a 180°) A B a C D

16. 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 6 Perimeter of Trapezium = 3 + 4 + 5 + 6 = 18cm

17. 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 .

18. Kite Formula Diagonal Method : Area of Kite = ½ X d1 X d2 Trigonometry Method: Area of Kite = a X b X SinC Perimeter 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 4cm DM : 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

19. Complex Quadrilaterals When two sides cross over , you call it a " Complex " or " Self-Intersecting ". For example : They still have 4 sides , but two sides cross over .

20. Any Questions? Thankyou!