Question

What is the area of the shaded segment?

• A. $1$ $m^2$
• B. $2$ $m^2$
• C. $3$ $m^2$
• D. $4$ $m^2$

Answer 1

The correct option is A $1$ $m^2$

From figure, we have

$A_{sector}=\frac{n}{360}\pi r^2$
$=\frac{30}{360}\pi 4^2$
$=4.18$ $c{m}^2$
$A_{triangle}=\frac{1}{2}bh$
$b=sin{60}^0\ast 4=$$2\sqrt{3}$
$h=cos{60}^0\ast 4=$$2$
$A_{triangle}=\frac{1}{2}bh$
$=$ $\frac{1}{2}2\sqrt{3}\times 2$
$=$ $3.46$
$A_{segment}=4.18-3.46\approx 1m^2$