00:01
Okay, so for this problem, we are given an equilateral triangle in which the apathom of this triangle is equal to 3 meters.
00:14
And using this information, we're told to find the area of the triangle.
00:20
So, we know that the area of triangle is equal to...
00:30
You'll write down actually the area of any polygon is equal to one half the apathym times the perimeter.
00:41
So because we're already given the apathym, we just need to find the perimeter.
00:45
And the perimeter of any polygon is equal to the number of sides times the side length.
00:56
So you can see in the diagram here, from proper.
01:03
Of equilateral triangles, we know that each angle is equal to 60 degrees.
01:12
So if we drew a line from one vertex to the center point here, you can see we would create this right triangle.
01:27
And this line that we drew would actually bisect one of the angles.
01:33
And when you bisect an angle, basically bisect an angle, basically.
01:36
Create a new angle, which i'll draw this bigger over here, so it's easier to see.
01:43
We've created this new angle down here, which i'll call theta.
01:51
This is going to be equal one half of the bisected angle.
02:00
So if we know that each angle of the triangle up here is equal to 60 degrees, then we know that theta, is equal to one half of 60 degrees.
02:15
So it's equal to 30 degrees.
02:18
And we know from the diagram that this is the apathem, and this length right here, because apathems go from the center point to the midpoint of a side, we know that this is equal to one half the length of the side.
02:36
So we know from properties of 30, 60, 90 triangles.
02:46
I forgot to show the 90, 30, 60, 90 triangles...