00:01
In this problem, we're asked to find the area of this rhombus, given that the angle is 120 degrees, and that each side is equal to 6 centimeters.
00:12
We can find the area of a rhombus by multiplying 1 half by the first diagonal, multiplied by the second diagonal.
00:24
First, let's find the values of d1 and d2.
00:28
Notice that these two diagonals bisect each other.
00:31
So this triangle here, i know that i am drawing in blue, is a right triangle, with sides half d1, half of d2, and the hypotenuse of 6.
00:45
To make things clear, i will redraw this triangle.
00:56
This is a right triangle with a height of half d2, a base of half of d1, and a hypotenuse of 6.
01:13
Since the angle was bisected by the second diagonal, this is 120 divided by 2 or 60 degrees.
01:24
Since the sum of all these angles has to be equal to 180 degrees, this means that this last angle is 30 degrees.
01:32
This is enough information to find the values of d1 and d2.
01:39
First, let's find the value of d1 by using the sign rule.
01:51
We know that sign of 60.
01:55
Is equal to the opposite side divided by the hypotenuse...