The trick in many area problems is to make a plan and think of ways to add and subtract calculable areas to find difficult to find areas. For example, a segment is just a sector minus a triangle.
One of the tasks students are assigned today is to find the measure of an angle given information about the area of a sector:
So, We would compare the area of the sector to the area of the circle
, so since we have
Now, this means that the shaded area, as a fraction of the total area of the circle is
So, since the shaded area is 5/24 of the area of the circle, the central angle must make up 5/24 of 360 degrees, so we find
So, the value of , or the central angle of the sector is
Tonight's assignment is to complete 8.6 on p. 439: 1-12, 17-22