Question

define area of a polygon state formula for the area of equilateral triangle

Answer 1

Area of polygon is equals to sum of areas of triangles in which it can be divided, required no other shape in it.
For example,
See the above attachment.
Area of octagon = Sum of areas of the 6 triangles.

Area of an equilateral triangle
$= \sqrt{s(s - a)(s - b)(s - c)} \\ but \: \: a = b = (equilateral \: \: triangle) \\ so \\ = \sqrt{ \frac{3a}{2} (3a \div 2 - a)(3a \div 2 - a)(3a \div 2 - a)}\\ (semiperimeter = \frac{a + a + a}{2} = \frac{ 3a}{2}) \\ = \frac{ \sqrt{3} }{4} {a}^{2}.$

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