Mathematics — Standard (041) — CBSE Class 10 board question

Given: Radius (r) = 5.6 m, Perimeter of sector = 20.0 m

Step 1: Find the arc length.

Perimeter of sector = 2r + arc length (l)

$$20.0 = 2 \times 5.6 + l$$

$$l = 20.0 - 11.2 = 8.8 \text{ m}$$

Step 2: Find the angle θ of the sector.

$$l = \frac{\theta}{360} \times 2\pi r$$

$$8.8 = \frac{\theta}{360} \times 2 \times \frac{22}{7} \times 5.6$$

$$8.8 = \frac{\theta}{360} \times 35.2$$

$$\theta = \frac{8.8 \times 360}{35.2} = 90°$$

Step 3: Find the area of the sector.

$$\text{Area} = \frac{\theta}{360} \times \pi r^2 = \frac{90}{360} \times \frac{22}{7} \times 5.6 \times 5.6$$

$$= \frac{1}{4} \times \frac{22}{7} \times 31.36 = \frac{1}{4} \times 98.56 = \mathbf{24.64 \text{ m}^2}$$

Source: Chapter 11, Section 11.1 — Areas of Sector and Segment of a Circle

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• Key formula: Perimeter of sector = 2r + arc length. Students often forget the two radii and write only the arc length — this loses marks.
• Find arc length first, then back-calculate θ (or skip θ entirely and use the shortcut: Area = ½ × l × r = ½ × 8.8 × 5.6 = 24.64 m²). The shortcut is faster and equally valid.
• Always use π = 22/7 unless the question says otherwise.
• Show each step clearly; CBSE awards step marks even if the final answer has an arithmetic slip.