The height of an equilateral triangle is 6 cm. Find its area. [Take $\sqrt{3}$ = 1.73.]

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Solution

Altitude = Height = 6 cm
Let length of side be 'a'

So , $fraction numerator square root of 3 over denominator 2 end fraction a$ = 6
So a = $fraction numerator 12 over denominator square root of 3 end fraction$
So a = $4 \sqrt{3}$ cm

This 'a' is the length of the side

Now, $A r e a = \frac{\sqrt{3}}{4} \times a^{2}$

$A r e a = \frac{\sqrt{3}}{4} \times (4 \sqrt{3})^{2}$

$A r e a = \frac{\sqrt{3}}{4} \times 16 \times 3$

So, $A r e a = \sqrt{3} \times 4 \times 3$

So, $A r e a = 12 \sqrt{3}$

So, $A r e a = 12 \times 1.732$

So, $A r e a = 20.784 c m^{2}$

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