Find the area of an isosceles triangle if the side is 40 and the apex angle is 120 degrees.

It follows from the condition of our problem that the length of each of the lateral sides is 40, because this triangle is isosceles.

But we know well from the school geometry course that the area of a triangle can be calculated using half of the product of any two sides and the sine of an angle that should lie between the selected sides.

Let us find out what the area will be equal to in this case, when from the condition of the problem we know that the angle between the sides is 120 °:

1/2 * 40 * 40 * √3 / 2 = 400√3.

Answer: 400√3.