00:02
Here we have a kite that's been inscribed in a circle.
00:09
And we need to find the area of the shaded region.
00:13
And we don't really have a formula for those little shaded pieces.
00:19
But we do have a formula that we can use to find the area of the kite shape and the area of the circle.
00:31
And then we can find the difference to find the shaded pieces.
00:35
There are a few things that are helpful to know ahead of time, and one of them is the inscribed angle theorem.
00:45
The inscribed angle theorem states that the measure of the inscribed angle is half the measure of the intercepted arc.
00:53
So in reference to this angle right here, this angle right here is half the measure of its intercepted arc.
01:03
Now the intercepted arc would be this arc here.
01:09
Since this line right here is a diameter, it cuts the circle in half, which means that this intercepted arc is 180 degrees, which means this angle is 90 degrees.
01:27
And the other triangle has the same situation on the top part, so this angle here is also 90 degrees, which means that these are right triangles, and finding the area of those right triangles becomes a lot easier because, we have the base and we have the height.
01:48
So the area of our triangles, now we have two of them, so i'm going to double this, is two times one -half times three times four.
02:02
So the triangle shapes, which make up the kite, together make up the kite, end up taking an area of 12.
02:16
Now the area of the circle can be found by using pythagran 3 ,000...