Answer
$273$ m$^{2}$
Work Step by Step
Converting the angle to decimal degrees:
$21^{\circ}40'=21(\frac{40}{60})=21.67^{\circ}$
Now converting the angle to radians:
$21.67^{\circ}=21.67(\frac{\pi}{180})=0.378$ radian
The formula for the area of a sector is $A=\frac{1}{2}r^{2}\theta$ where $r$ is the radius and $\theta$ is the central angle in radians.
Substituting the values of $r$ and $\theta$ into the formula and solving using a calculator:
$A=\frac{1}{2}r^{2}\theta=\frac{1}{2}(38)^{2}(0.378)\approx273$ m$^{2}$
