00:01
All right, we're going to take a look at a real -life application of area of a sector.
00:06
What we're looking at is a windshield wiper blade.
00:11
I'm an artist here.
00:15
But that windshield wiper blade is 38 inches from the top to the pivot point.
00:30
And then we're also told that it is 14 inches from the bottom of the blade to the pivot point.
00:42
All right, and so when this blade pivots, obviously this top is going to make its way.
00:50
Cross the bottom blade will also make its way across because it is pivoting from this bottom point right here.
00:59
And when it pivots, it does so at an angle of 135 degrees.
01:15
So when we're asked to find the area that the blade actually sweeps, we want to keep in mind that we are not finding the area of this sector as a whole.
01:25
Because the blade itself is only going to sweep across this top portion here and will not include this bottom sector here.
01:33
So in order to find just this piece here, note that that is not a sector.
01:39
The shape of that, the area that we're trying to find kind of look something like this.
01:44
Okay, so rather than trying to find the area of an awkward shape such as that, what we'll do in fitzsad is find the area of this entire sector and the area of the smaller sector here that is not swept by the blade.
02:00
If we subtract the two of them, it'll leave us with this shape here and its area.
02:06
So let's begin with the area of a sector formula.
02:10
Area of a sector formula is one -half r squared theta, where r is the radius, and theta is the angle in radiance.
02:20
So we do have to be careful our angle is provided in degrees here.
02:23
So we're going to start with the larger of the sectors.
02:28
I'll call that capital r.
02:32
Radius of 38...