Question 197

If the altitude of an equilateral triangle is 12√3 cm, then its area would be :

Solution

Let each side of the equilateral triangle be $$a$$

The altitude of an equilateral triangle bisects the opposite side.

=> $$(\frac{a}{2})^2 + (12\sqrt{3})^2 = a^2$$

=> $$a^2 - \frac{a^2}{4} = 432$$

=> $$a^2 = \frac{1728}{3}$$

Area of equilateral triangle = $$\frac{\sqrt{3}}{4} * a^2$$

= $$\frac{\sqrt{3}}{4} * \frac{1728}{3}$$

= $$144\sqrt{3}$$

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