00:01
We now determine the area of the shaded region in the diagram.
00:05
So we write area of shaded region and that equals.
00:19
Basically, it's the bigger area minus the smaller area.
00:23
Here we have a semicircle that would be the bigger area.
00:27
And inside the semicircle, we have a triangle.
00:30
So that would be the smaller area.
00:33
So we can write the area of the shared region and that equals area of semicircle minus area of the triangle inside that is area of triangle abc.
00:53
So here we have to do a couple of things.
00:56
That is we have to determine area of semicircle as well as area of triangle abc and then do the subtraction.
01:03
So we will do one by one.
01:05
So first i'm going to determine area of semicircle.
01:09
We know the formula for area of circle and that equals pi r squared where r represents the area of the circle.
01:28
An area of semicircle will be half the area of a circle.
01:33
So we write area of a semicircle and this equals half the area of a circle.
01:42
The area of circle is pi r squared.
01:45
So it's basically pi r squared divided by 2 is the area of the semicircle.
01:53
And for this we need the radius of the semicircle.
01:56
Let's see how to determine the radius of this semicircle.
02:00
Now looking at this diagram, we have a triangle which is formed inside the semicircle.
02:08
Or otherwise we can see that an angle is formed inside this semicircle.
02:12
So going by the geometry, whenever an angle is formed inside a semicircle, that angle equals 90 degree or otherwise we see that it is a right angle.
02:25
And so this means this triangle is a right triangle.
02:29
So we are going to consterned this right triangle and determine ab, which represents the hypotenuse of the right triangle.
02:37
I'm going to draw this right triangle over here.
02:41
So we have this triangle.
02:52
Now i mark the endpoints that is ab, which forms the diameter of the semicircle.
03:00
So here it is a.
03:01
This is b.
03:02
And this one is the midpoint.
03:05
Oh.
03:06
And then the point with it touches the semicircle is c.
03:10
So this is the right angle...