# Find the area of an isosceles triangle if its lateral side is 6 cm and the apex angle is 60 degrees.

The sum of all interior angles in a triangle is 180 degrees. Since the triangle is isosceles, the angles at the base are equal, we find their value:
1) (180-60): 2 = 120: 20 = 60 degrees.
All angles of a triangle are 60 degrees. It follows that the triangle is equilateral.
We draw the height in a triangle to any of the bases. It turned out a right-angled triangle, where the angles are 30, 60 and 90 degrees, sides are 6, 3 and x cm.We find x:
2) x = ((√3): 2) * 6 = 3√3 cm – the height of the triangle.
Find the area:
3) S = 1/2 * a * h = 1/2 * 6 * 3√3 = 3 * 3√3 = 9 √3 cm2.
Answer: The area of a triangle is 9√3 cm2.

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