Area and Arc Length of Sectors

Arc Length of a Sector

Area of a Sector

Manipulating the Sector Formulae

Sectors and their Formulae

Prerequisite Knowledge

• 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;

Success Criteria

• Calculate arc lengths, angles and areas of sectors of circles
• Understand and use standard mathematical formulae; rearrange formulae to change the subject
• Know the difference between an equation and an identity; argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments

Key Concepts

• A sector is a fraction of 360° of the entire circle.
• Students need to have a secure understanding of using the balance method when rearranging formulae. Recap inverse operations, e.g., x^2=>√x.
• When generating formulae it is important to associate mathematical operations and their algebraic notation with key words.

Common Misconceptions

• 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.
• Students often have difficult generating formulae from real life contexts. Encourage them to carefully break down the written descriptions to identify key words.