A sector of a circle of radius 14 cm has a perimeter of 50 cm (two radii plus the arc). What is the area of the sector? Take $\pi = \frac{22}{7}$.

Explanation

1. 01

   Arc length = $50 - 2 \times 14 = 22$ cm.

2. 02

   The full circumference is $2 \times \frac{22}{7} \times 14 = 88$ cm, so the sector is $22/88$ = ¼ of the circle.

3. 03

   Area = $\frac{1}{4} \times \frac{22}{7} \times 14 \times 14 = 154$ cm². (Shortcut: area = ½ × arc × radius = $\tfrac{1}{2} \times 22 \times 14$.)