Question 133

The height of an equilateral triangle is 15 cm. The area of the triangle is

Solution

AD = 15 cm and ABC is equilateral triangle

In $$\triangle$$ADC

=> $$tan \angle ACD = \frac{AD}{DC}$$

=> $$tan 60 = \frac{15}{DC}$$

=> DC = $$\frac{15}{\sqrt{3}} = 5\sqrt{3}$$

=> BC = 2*DC = $$10\sqrt{3}$$

Area of $$\triangle$$ ABC = $$\frac{\sqrt{3}}{4} * side^2$$

= $$\frac{\sqrt{3}}{4} * (10\sqrt{3})^2$$

= $$75\sqrt{3} cm^2$$

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