A sector of a circle is bounded by two radii 7cm long and an arc length 6cm. Find the area of the sector.

A.

42cm2

B.

3cm2

C.

21cm2

D.

24cm2

E.

12cm2

Correct answer is C

Length of arc = \(\frac{\theta}{360}\) x 2\(\pi\)r = 6

\(\theta\) x 2\(\pi\)r = 360 x 6

\(\theta\) = \(\frac{360 \times 6}{2\pi r}\)

Area of the sector = \(\frac{\theta}{360}\) x \(\pi\)r2

\(\frac{360 \times 6}{2\pi r}\) x \(\frac{1}{360}\) x \(\pi\)r2 = r

= 3 x 7

= 21cm2