proof the area of equilateral triangle
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In equilateral triangle have all side are equal so this os why area os 3×all sides
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The area of an equilateral triangle can be found by using the Pythagorean formula:
a2 = (a/2)2 + h2
a2 = a2/4 + h2
a2 − a2/4 = h2
4a2/4 − a2/4 = h2
3a2/4 = h2
h = √(3a2/4)
h = (√(3)×a)/2
Area = (base × h)/2
base × h = (a × √(3)×a)/2 = (a2× √(3))/2
Dividing by 2 is the same as multiplying the denominator by 2. Therefore, the formula is
a2 = (a/2)2 + h2
a2 = a2/4 + h2
a2 − a2/4 = h2
4a2/4 − a2/4 = h2
3a2/4 = h2
h = √(3a2/4)
h = (√(3)×a)/2
Area = (base × h)/2
base × h = (a × √(3)×a)/2 = (a2× √(3))/2
Dividing by 2 is the same as multiplying the denominator by 2. Therefore, the formula is
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