Determine the area of an equilateral triangle whose side length is a

Answers (1)
S safeer

Side AC =a. D is the midpoint of AB and CD is the perpendicular height.

AD=a/2

By Pythagoras theprem

\\CD^2=\sqrt{AC^2-AD^2}\\\\=\sqrt{AC^2-AD^2}\\\\=\sqrt{a^2-\frac{a^2}{4}}=\frac{\sqrt{3}}{2}a

Therefore the area is

\\frac{1}{2}\times base\ lenght\times height \\\\=\frac{1}{2}\times a\times\frac{\sqrt{3}}{2}a=\frac{\sqrt{3}}{4}a^2

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