Answer
$\theta=0.5$ radian
$A= 16$ square units
Work Step by Step
Part 1:
To find the central angle $\theta$, we use the formula $s=r\theta$ where $s$ is the arc length, $r$ is the radius and $\theta$ is the central angle in radians.
Next, we rearrange the formula to $\theta=\frac{s}{r}$ because $s$ and $r$ are known and $\theta$ is the unknown.
Substituting the values of $r=8$ and $s=4$ into the formula and solving:
$\theta=\frac{s}{r}=\frac{4}{8}=0.5$ radian
Part 2:
To find the area of the sector, we use the formula $A=\frac{1}{2}rs$ where $r$ is the radius and $s$ is the arc length.
Substituting the values of $r$ and $s$ into the formula and solving:
$A=\frac{1}{2}rs=\frac{1}{2}(4)(8)= 16$ square units