![ 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](https://image.slidesharecdn.com/quadrilateral-presentation-150208045701-conversion-gate01/85/Quadrilateral-presentation-11-320.jpg)
Quadrilateral presentation
- 1. QUADRILATERALQUADRILATERAL Mathematics (MTH 30104) HOR WENG LIM WAH YUN CHEN KHOO MING SEN CHAI CHIN EE AARON NGU NGUOK SOON
- 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. 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°
- 4. Types of Quadrilateral Parallelogram Square Rectangle
- 6. 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.
- 7. 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 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. 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
- 15. Alternate Angle a 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 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. Thank You Very Much ! That's all for Quadrilaterals