Question

Determine the area of the shaded segment.

• A. $10$
• B. $11$
• C. $12$
• D. $13$

Answer 1

The correct option is B $11$

$A_{segment}=A_{sector}-A_{triangle}$
$A_{sector}=\frac{n}{360}\pi r^2$
$=\frac{60}{360}\pi 6^2$
= 18.84 $c{m}^2$
$A_{triangle}=\frac{1}{2}bh$

$b=sin{60}^0\ast 6=$$3\sqrt{3}$
$h=cos{60}^0\ast 6=$$3$
$A_{triangle}=\frac{1}{2}bh$
= $\frac{1}{2}3\sqrt{3}\times 3$
= $7.79$
$A_{segment}=18.84-7.79\approx 11$