Answer:
[tex]\dfrac{9\pi}{2}[/tex]
Step-by-step explanation:
[tex]\text{Solution: }\\\text{Area of circle = }\pi r^2\\[/tex]
[tex]\text{A circle equals 360}^\circ,\text{ so area of circle = area subtended by }360^\circ.[/tex]
[tex]\text{or, Area subtended by }360^\circ=\pi (6)^2=36\pi\\\\\text{or, Area subtended by }1^\circ = \dfrac{36\pi}{360}\\\\\text{or, Area subtended by 45}^\circ=\dfrac{36\pi}{360}\times45^\circ\\\\\therefore\ \text{Area of sector = }\dfrac{45\pi}{10}=\dfrac{9\pi}{2}[/tex]
Here, I used the unitary method to solve for the area of the sector but you may use the formula:
[tex]\text{Area of sector = }\dfrac{\theta}{360^\circ}\times\pi r^2\\\\\text{Here, }r\text{ is the radius of circle and }\theta\ \text{is the angle of sector. In this case, central}\\\text{angle (angle of sector) is equal to the measure of the arc, i.e. }\theta=45^\circ.[/tex]
