Area of 2D Shapes

Students learn how to find the area of various 2D shapes  parallelograms, trapezia, compound shapes and circles.  Throughout the topic links are made to algebraic reasoning and estimation.  This topic takes place in Term 1 of Year 9 and links to  volume and surface area later on.


Area of 2D Shapes Lessons


Prerequisite Knowledge

  • Know and apply formulae to calculate the area of rectangles
  • Calculate the perimeters of 2D shapes, including composite shapes;
  • Compare and order lengths, mass, volume / capacity and record the results using >, < and =
  • Measure, compare, add and subtract: lengths (m/cm/mm); mass(kg/g); volume/capacity (l/ml)
  • Identify and apply circle definitions and properties, including: centre, radius, chord, diameter, circumference, tangent, arc, sector and segment

Success Criteria

  • Know and apply formulae to calculate: area of triangles, parallelograms and trapezia;
  • Know the formulae: circumference of a circle = 2πr = πd, area of a circle = πr2; calculate: perimeters of 2D shapes, including circles; areas of circles and composite shapes;
  • Calculate arc lengths, angles and areas of sectors of circles


Key Concepts

  • Demonstrate a triangle as being half a rectangle so students know to use the perpendicular height in their calculation. Demonstrate a parallelogram as having an equal area to a rectangle.
  • To calculate the area of composite rectilinear shapes have students break them up in different ways.
  • A sector is a fraction of 360° of the entire circle.

Common Misconceptions

  • Students often confuse area and perimeter.
  • When calculating the area of a triangle or parallelogram students tend to use the slanted height rather than the correct perpendicular height.
  • Arc length and area of a sector are often rounded incorrectly. Encourage students to evaluate as a multiple of pi and calculate the decimal at the end.

 

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