Problem 39

Answer

Given that the arc length $L = 4$ cm and the central angle $\theta = 2$ radians, we can use the formula for the area of a sector, which is $A = \frac{1}{2}r^2\theta$. Since the arc length is also given by $L = r\theta$, we can solve for $r$ to find the radius of the circle. Substituting $L = 4$ cm and $\theta = 2$ radians into $L = r\theta$, we get $4 = r \times 2$, which gives us $r = 2$ cm.

Now, substituting $r = 2$ cm and $\theta = 2$ radians into the formula for the area of a sector, we get $A = \frac{1}{2} \times 2^2 \times 2 = 4$ cm2.

Therefore, the area of the sector is $\boxed{4}$ cm2.