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
4 Part Lesson
Area of Parallelograms and Trapezia
4 Part Lesson
Area of Composite Shapes
4 Part Lesson
Circumference of Circles Problems
4 Part Lesson
Circumference of Circles
4 Part Lesson
Area of Circles Problems
4 Part Lesson
Area of Circles
Additional Resources
Extended Learning
Circumference of Circles
Revision
Area of 2D Shapes
Revision
Problems with Circles
Revision
Area of Triangular Shapes

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.

Mr Mathematics Blog

Volume of Similar Shapes

In this lesson, we learn about the length and volume scale factor of 3D shapes and the relationship between them.

Solving Simultaneous Equations by Substitution

How to solve simultaneous equations using the substitution method.

Using Box Plots to Interpret Sets of Data

How to compare datasets using box and whisker diagrams.