Perimeter of a sector
The perimeter of a sector is made from the curved arc plus the two straight radii. Use this worksheet to practise finding arc length, adding the two radii, and rounding your answers to 1 decimal place.
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Topic guide
What this worksheet practises
This worksheet helps you practise calculating the perimeter of a sector. The perimeter is the total distance around the outside edge of the shape. For a sector, this distance is made up of the curved arc length plus the two straight radii. You must remember to add the two radii, rather than just calculating the arc length.
Key method
To find the perimeter, first calculate the arc length, and then add the two straight sides.
The formulas you need are:
Arc length = angle ÷ 360 × 2 × π × r
Perimeter of sector = arc length + 2r
When calculating, you can use either π = 3.142 or your calculator's π button. These values might give answers that round slightly differently, but both methods are perfectly acceptable.
Worked example
A sector has a radius of 8 cm and an angle of 90°. Calculate its perimeter to 1 decimal place.
Step 1: Find the arc length.
Arc length = 90 ÷ 360 × 2 × π × 8
Arc length ≈ 12.6 cm
Step 2: Add the two radii to find the total perimeter.
Perimeter = 12.6 + 8 + 8
Perimeter ≈ 28.6 cm
Useful tips
Write down the arc length as a separate step before adding the radii. Keeping the steps clear makes it much easier to avoid mistakes. Make sure to round your final answer to 1 decimal place.
Common mistakes to avoid
The most common mistake is finding only the curved arc length and forgetting to add the two straight radii. Remember, the perimeter is the entire boundary of the shape. Another common error is using the formula for the area of a circle instead of the circumference when finding the arc length.
How to check your answer
Look closely at your shape. If the two straight sides are 8 cm each, those alone add up to 16 cm. Your final perimeter must definitely be larger than 16 cm!