Answer:
Explanation:
There's a fact hidden in the diagram that if you do not know it, the problem will be very difficult to solve. The fact is this. If a 60 degree angle is enclosed by the hypotenuse and the other of side of the 60 degree angle. the hypotenuse is 2 times the length of the side.
In this case the hypotenuse is 12. The given side is 6. The third side of the right triangle is 12^1 - 6^2 = 144 - 36 = 108
The length of the third side is sqrt(108) = 6*sqrt(3)= 10.39
The area of one of the triangles is 1/2 * 6 * 10.39 = 31.18
The area of two of the triangles is 2 * 31.18. = 62.36
Now you you have to do is find the area of the unshaded sector
Area = given angle / 360 * pi * r^2
Area = 120/360 * 3.14 * 6^2
Area = 37,68
The area of the shaded part = the area of the 2 triangles - the unshaded sector
The area of the shaded part = 62.36 - 37.68 = 24.68