• Quick retrieval from earlier learning (Arc length and sector area; Area of a triangle: ½ab sin C). Students answer on mini whiteboards.
• Show answers together and note who needs support in the main task.

1. A sector has radius 15 cm and angle 45°. Find the arc length in cm, rounded to 1 decimal place. → 11.8Prompt: Arc length = (θ/360) × 2πr.
2. Two sides of a triangle are 16 cm and 18 cm with an angle of 127° between them. Find the area to 1 decimal place. → 115Prompt: Area = ½ab sin C, where C is the angle between a and b.
3. Find the area of a sector with radius 4 cm and angle 60°. Round to 1 decimal place. → 8.4Prompt: Sector area = (θ/360) × πr².

• Show a photo of a building, a tile pattern or a road sign and ask what shapes and angles students can spot.
• Share the objective: Find the area of a circular segment. Read the success criteria together.

• Work through the example out loud, saying why you do each step, not just what you do.
• Example: A chord cuts off a minor segment of a circle of radius 15 cm. The chord subtends 50° at the centre. Find the area of the segment to 1 decimal place.
• Step 1: 50/360 × π × 15² − ½ × 15² × sin 50°
• Step 2: ≈ 12 cm²
• Answer: 12
• Pause after each step and ask a student to say what comes next.

• Do these together. Students try each step on whiteboards before you reveal it.
• Use the hints as prompts rather than giving the answer.

1. A chord cuts off a minor segment of a circle of radius 7 cm. The chord subtends 110° at the centre. Find the area of the segment to 1 decimal place. → 24Prompt: Segment = sector − triangle.
2. A segment of a circle of radius 9 cm has angle 2.5 radians at the centre. Find its area to 2 decimal places. → 77.01Prompt: In radians: segment area = ½r²(θ − sin θ).

• Students work on the student sheet. Circulate and check the first two answers of every student early.
• Students who finish: write a question of their own for a partner, with the answer.

The 8 questions are on the student sheet below, with answers in the key.

• Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.

1. A segment of a circle of radius 7 cm has angle 0.9 radians at the centre. Find its area to 2 decimal places. → 2.86Prompt: In radians: segment area = ½r²(θ − sin θ).
2. A chord cuts off a minor segment of a circle of radius 6 cm. The chord subtends 135° at the centre. Find the area of the segment to 1 decimal place. → 29.7Prompt: Segment = sector − triangle.

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-11.