Answer
$\dfrac{169}{6} \pi \ m^2$
Work Step by Step
Let $A$ be the area of a sector of a circle . The area $(A)$ of a sector of a circle whose radius is $r$ is given by: $A=\pi r^2 \times \dfrac{Measure \ of \ the \ arc}{360^{\circ}}...(1)$
We are given that radius $r=13 \ m (\because r=\dfrac{d}{2}=\dfrac{26}{2}=13)$ and $Measure \ of \ the \ arc=180\circ-120\circ=60^{\circ}$
Plug the data in the equation (1) to obtain:
$A=\pi (13)^2 \times \dfrac{60^{\circ}}{360^{\circ}}$
Therefore, we get , $Area=\dfrac{169}{6} \pi \ m^2$
