Question

In a circle with radius $5.7cm$, the perimeter of a sector is $27.2cm$. Find the area of this sector.

• A. $97.52c{m}^2$
• B. $57.52c{m}^2$
• C. $77.52c{m}^2$
• D. $87.52c{m}^2$

Answer 1

Answer: (C)

$77.52c{m}^2$

$R=5.7cm$

Perimeter = $R\theta =27.2cm$

$\therefore R\theta =27.2cm$

$\theta ={\left(\frac{27.2}{5.7}\right)}^c$

$\therefore$ Area of sector $=\frac{1}{2}{R}^2\theta$

$=\frac{1}{2}\times (5.7{)}^2\times \frac{27.2}{5.7}$

$=\frac{5.7}{2}\times 27.2c{m}^2$

$=5.7\times 13.6=77.52c{m}^2$