AI generatedGeometry and measuresGCSE Higher

Area of a segment of a circle

Area of a segment of a circle.

  • Label the sides and angles before choosing a rule.
  • Sine rule: matching opposite pairs. Cosine rule: three sides or two sides and the included angle.
  • Use degree mode. Keep full calculator accuracy until the final rounding step.

Example 1

Find the area of the shaded minor segment. Give your answer to 1 decimal place.

Shaded minor segment45°4 cmO
Find the sector area.Find the triangle between the two radii.Subtract the triangle from the sector.
CalculatorKeep full accuracy, then round the final result.

Example 2

Find the area of the shaded minor segment. Give your answer to 1 decimal place.

Shaded minor segment46°5 cmO
Find the sector area.Find the triangle between the two radii.Subtract the triangle from the sector.
CalculatorKeep full accuracy, then round the final result.

Your turn

Question 1

Find the area of the shaded minor segment. Give your answer to 1 decimal place.

Shaded minor segment47°6 cmO
Check answer
Find the sector area.Find the triangle between the two radii.Subtract the triangle from the sector.
CalculatorKeep full accuracy, then round the final result.
Question 2

Find the area of the shaded minor segment. Give your answer to 1 decimal place.

Shaded minor segment48°7 cmO
Check answer
Find the sector area.Find the triangle between the two radii.Subtract the triangle from the sector.
CalculatorKeep full accuracy, then round the final result.
Question 3

Find the area of the shaded minor segment. Give your answer to 1 decimal place.

Shaded minor segment49°8 cmO
Check answer
Find the sector area.Find the triangle between the two radii.Subtract the triangle from the sector.
CalculatorKeep full accuracy, then round the final result.
Question 4

Find the area of the shaded minor segment. Give your answer to 1 decimal place.

Shaded minor segment50°9 cmO
Check answer
Find the sector area.Find the triangle between the two radii.Subtract the triangle from the sector.
CalculatorKeep full accuracy, then round the final result.
Question 5

Find the area of the shaded minor segment. Give your answer to 1 decimal place.

Shaded minor segment51°10 cmO
Check answer
Find the sector area.Find the triangle between the two radii.Subtract the triangle from the sector.
CalculatorKeep full accuracy, then round the final result.
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