Since we know a circle has 360 degrees, the sector bounded by a 90 degree arc will be a quarter of circle (360/90 = 4). Then, to calculate the area of that sector, we can calculate the total area of the circle of radius 10, and then divide it by 4.
The area of a cirlce of radius r is:
[tex]A=\pi r^2[/tex]
Then, the area of the sector would be:
[tex]A_s=\frac{\pi r^2}{4}[/tex][tex]A_s=\frac{\pi(10m)^2}{4}=\frac{100\pi}{4}m^2[/tex][tex]A_s=25\pi m^2[/tex]
