EDEXCEL GCSE FOUNDATION MATHS - What is the Area of a Sector

Edexcel GCSE Foundation Maths - What is the Area of a Sector?

What is a sector?

A sector is a part of a circle enclosed by two radii and the arc between them. Imagine slicing a pizza into equal slices. Each slice is a sector!

Calculating the area of a sector

To calculate the area of a sector, you need to know:

• The radius (r) of the circle
• The angle (?) of the sector

The formula for the area of a sector is:

Area of sector = (?/360) * ?r²

Explanation of the formula:

• (?/360): This represents the fraction of the whole circle that the sector covers. The angle of the sector (?) is divided by 360 degrees (the total degrees in a circle).
• ?r²: This is the formula for the area of the whole circle.
• Multiplying (?/360) by ?r² gives you the area of the sector, which is a fraction of the whole circle's area.

Example:

Let's say you have a sector with a radius of 5 cm and an angle of 60 degrees.

1. Calculate the fraction of the circle: 60 degrees / 360 degrees = 1/6
2. Calculate the area of the whole circle: ? * (5 cm)² = 25? cm²
3. Multiply the fraction of the circle by the area of the whole circle: (1/6) * 25? cm² = (25/6)? cm²

Therefore, the area of the sector is (25/6)? cm².

Important points to remember:

• The angle ? must be in degrees.
• You can use the value of ? as 3.14 or 22/7.

Practice questions:

1. A sector has a radius of 8 cm and an angle of 45 degrees. Calculate the area of the sector.
2. A sector has an area of 12? cm² and an angle of 90 degrees. Calculate the radius of the sector.

Key takeaways:

• A sector is a part of a circle.
• The area of a sector is a fraction of the area of the whole circle.
• Use the formula (?/360) * ?r² to calculate the area of a sector.