Find the area of an equilateral triangle if its side is 80mm.

1. Vertices of the triangle – A, B, C. AB = BC = AC = 80 centimeters. BE – height. S is the area of the triangle.
2. Each of the angles of this triangle (∠А, ∠В, ∠С), according to its properties, is 60 °.
3. We calculate the length of the side AB through the sine ∠A of the right-angled triangle ABE:
∠А = 60 °. Sine 60 ° = √3 / 2.
BE: AB = √3 / 2.
BE = AB x √3 / 2 = 80 x √3 / 2 = 40√3 centimeters.
4. S = AC / 2 x BE. AB = AC = 80 centimeters.
S = 80: 2 x 40√3 = 1600 √3 centimeters².
Answer: S equals 1600 √3 centimeters².