# The generatrix of the 12 cm cone is inclined to the base plane at an angle of 60 degrees.

**The generatrix of the 12 cm cone is inclined to the base plane at an angle of 60 degrees. Find the area of the base of the cone.**

The base of the cone is a circle, and therefore it is calculated by the formula: S = pi * r2, where S is the area of the circle, pi is the number of pi, and r is the radius of the circle.

The generatrix of the cone and its radius form a right-angled triangle with an angle at the base of 60 degrees, which means that the 2nd angle is equal to: 180 – 60 – 90 = 30 degrees.

And we know that the leg of a right-angled triangle, which lies against an angle of 30 degrees, is twice less than the hypotenuse and is equal to 12/2 = 6 cm.

Now we know the radius of the circle (6 cm) and can calculate its area: S = 3.14 * 36 ~ 113 cm2.

Therefore, our answer is 113 cm2.