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MEASUREMENT Area

MEASUREMENT Area. Area. The area of a figure or shape is the amount of 2-dimensional space taken up by that figure Area is measured in square units m m 2 c m 2 m 2 km 2 o r just units squared Hectare (ha) is also used with 1ha = 10 000 m 2

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MEASUREMENT Area

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  1. MEASUREMENT • Area

  2. Area • The area of a figure or shape is the amount of 2-dimensional space taken up by that figure • Area is measured in square units • mm2 • cm2 • m2 • km2 • or just units squared • Hectare (ha) is also used with 1ha = 10 000 m2 • Area can be defined as the number of square units contained within a shape’s boundary. • 2-d shapes are sometimes called ‘plane’ shapes

  3. The Unit Square If this represents 1 square unit 4 square units This shape is then made up of 8 of these single units. Equivalent to 4 ⨯ 2 = 8 square units 2 square units To work out the area of any shape, you can reduce the problem into this simplified format.

  4. Area Conversions To convert between square units, the base conversion factor must be squared. 10mm 100cm A = 1cm2 or A = 100mm2 A = 1m2 or A = 10000cm2 1m 1cm 10mm 100cm 1cm 1m Conversion factor 1 cm = 10mm 1 cm2 = 102 mm2 = 100 mm2 Conversion factor 1 m = 100cm 1 m2 = 1002cm2 = 10000 cm2

  5. Area Conversions

  6. 15 minute activity Each group will be allocated a different 2-d shape - Square, rectangle, parallelogram, rhombus, triangle, circle In your groups I want you to investigate all the properties of your shape (ensure some are mathematical), and anything else interesting about your shape. You will be given an A4 sized piece of card to decorate your card. Feel free to make use of coloured pencils and pens. Prize tomorrow for the best looking and most informative poster.

  7. Area - Square • A square has the following properties. • 4 sided shape • Each side is the same length • Each internal angle is 90° • Opposite sides are parallel Area = base ⨯height = a ⨯ a = a2 a a Check out this website

  8. Area - Rectangle • A rectangle has the following properties. • 4 sided shape • Each internal angle is 90° • Opposite sides are parallel and are of equal length Area = base ⨯ height = a ⨯ b = ab b a Check out this website

  9. Area - Parallelogram • A parallelogram has the following properties. • 4 sided shape • Opposite sides are parallel and are of equal length • Opposite internal angles are equal • Opposite angles are supplementary i.e. add to 180° Area = base ⨯ height = a ⨯ b = ab b a Note: height is perpendicular height, not length of side Check out this website

  10. Area - Rhombus • A rhombus has the following properties. • 4 sided shape with all sides of equal length • Opposite sides are parallel • Opposite internal angles are equal • Adjacent angles are complementary i.e. add to 180° • Diagonals bisect each other at right angles Area = base ⨯ height = a ⨯ b = ab b a Note: height is perpendicular height, not length of side Check out this website

  11. Area -Trapezium • A trapezium has the following properties. • 4 sided shape • 1 pair of opposite sides parallel b Area = average (parallel sides) ⨯ height = h a Note: height is perpendicular height, not length of side Check out this website

  12. Area -Triangle • A triangle has the following properties. • 3 sided shape • 3 internal angles • The internal angles always add to 180° Area = = h a Note: height is perpendicular height, not length of side Check out this website

  13. Area –Circle A circle is • A set of points of equal distance from the centre Area = πor = π d r Note: a semi-circle (half a circle) is also known as a hemisphere Check out this website

  14. Area –Sector of a Circle If a sector has an angle at the centre equal to 𝞱, then what would the area of the sector be? Area sector = πr2 r 𝞱 r

  15. Summary

  16. Practice Problems Calculate the area of the following shapes: 7.5 cm Find grey area What % is the blue area?

  17. Some Harder Practice Problems Calculate the area of the following shapes: A chocolate bar is wrapped in a rectangular piece of foil measuring 14cm by 20cm. Calculate the area of the piece of foil. How many pieces could be cut out from a larger sheet of foil measuring 2.4m by 1.4m? What is the total area of the shaded part of rectangle ACDB?

  18. Areas of Composite Shapes A composite shape (also called a compound shape) is made up of various parts. To find the area of a composite shape, find the areas of each individual shape, and either add or subtract as you need to. These are examples of composite shapes:

  19. Example: find the area of this shape Area of compound shape: = area of Rectangle + area of Triangle + area of semi-circle 2 cm 5 cm Area = b × h + ½ b × h + ½ π × r2 4 cm = 4 × 5 + ½ 4 × 2 + 0.5 π × (2)2 = 30.3 cm2 (1 dp)

  20. Example: Think of a typical running track. What is the perimeter? How long are the straight sections? Calculate the area enclosed by the track. 100 m Acircle + Arectangle = Atotal d = ? 3183.1 + 6366.2 = 9549.3 m2 (1dp)

  21. Example: A glass porthole on a ship has a diameter of 28 cm. It is completely surrounded by a wooden ring that is 3 cm wide. a.) Calculate the area of glass in the porthole b.) Calculate the area of the wooden ring A = πr2 r = 14 cm A = π (14)2 A = 616 cm2 Area of porthole = πr2 , r = 17 cm (including frame) = 908 cm2 Area of frame = 908-616 = 292 cm2

  22. Homework 2d shapes: Exercise F: Pages 170-171 Composite Shapes : Exercise G: Pages 172-174

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