Area of an equilateral triangle
The area of an equilateral triangle can be found by using the pythagorean formula:
Start with any equilateral triangle
Label the sides
Draw the perpendicular bisector of the equilateral triangle as shown below. Note how the perpendicular bisector
breaks down side a into its half or a/2
Now apply the pythagorean theorem to get the height (h) or the length of the line you see in red
a^{2} = (a/2)^{2} + h^{2}
a^{2} = a^{2}/4 + h^{2}
a^{2} − a^{2}/4 = h^{2}
4a^{2}/4 − a^{2}/4 = h^{2}
3a^{2}/4 = h^{2}
h = √(3a^{2}/4)
h = (√(3)×a)/2
Area = (base × h)/2
base × h = (a × √(3)×a)/2 = (a^{2}× √(3))/2
Dividing by 2 is the same as multiplying the denominator by 2. Therefore, the formula is
Fun math game: Destroy numbered balls by adding to 10
