In an isosceles triangle, the side is 10 and the angle opposite the base is 120 °. Find the area of a triangle divided by √3.

Let us denote the triangle by the letters ABC, where AB is the base of the triangular. Let’s draw the height CH.
S = 1/2 * AB * CH
Consider a triangle СBH
Angle B = 30 degrees. (An angle opposite an angle of 30 degrees is half the hypotenuse)
CH = 1 / 2BC
CH = 5
By the Pythagorean theorem, we find the BN leg.
ВН ^ 2 = ВС ^ 2-СН ^ 2 = 100-25 = 75
VN = 5 √ 3
AB = 10 √ 3
S = 1/2 * 10 √ 3 * 5 = 25 √3
We divide by the root of three by the condition
Answer: S = 25