00:01
Hello, welcome to this lesson.
00:02
In this lesson we are to find the area of the shaded portion.
00:12
So the best way of looking at this is to think of the portion in here.
00:22
The portion that i'm outlying with the green as six triangles.
00:37
Okay, so if we know the total area of the six triangles, you can subtract that from the area of the circle and we would, what was left, the remainder would become the area of the shaded portion.
00:58
So now we have a size of six and that gives the polygon a name as the hexagon.
01:08
Now the total angle, interior angle for this hexagon is 720 degrees.
01:19
And now the individual angles, that is this angle, is the 720 degrees on 6, no 66, yeah, just 6 of them.
01:36
And now this is equal to 120 degrees.
01:38
So each of these angles has got each of these angles is 120 degrees.
01:48
So the angle looks like this and this is 120 degrees.
01:54
This is 120 degrees.
01:58
But from extension it goes like this and it comes like this.
02:04
So it means that from the center of the circle, the angle formed here.
02:12
We are just driving through the center of that that should be 60 and this should be 60 okay then this two should be 60 so that we can have a equilateral triangle and because the angles are the same the length are also the same so we have six six throughout all right the radius is equally six and now we have a triangle like this and a collateral triangle we should be able to find the area of one of these so this is 60 that is 60 degrees so this is 60 and now what we do is that we can divide this into two so that we'll find the height because we need the height in other to get the area the area of the triangle is half base times height the base is six this side is six as well so if you divide it into two so that we can use the pythagrass theorem.
03:22
Let's label it a -o -b -c.
03:26
So the triangle a -c -o is what we'll use and now we know from pythagrass that the longest side which is the a -o squared is equal to the sum of squares of the other two...