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The perimeter of a sector of a circle of radius $21$ cm is $75$ cm. Find the area of the sector.
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(b) $\frac{\theta}{360} \times 2 \times \frac{22}{7} \times 21 + 42 = 75 \implies \frac{\theta}{360} = \frac{1}{4}$
Area of sector = $\frac{1}{4} \times \frac{22}{7} \times 21 \times 21 = \frac{693}{2}$ or $346.5$ cm$^2$
Area of sector = $\frac{1}{4} \times \frac{22}{7} \times 21 \times 21 = \frac{693}{2}$ or $346.5$ cm$^2$