If the alltitude of an equilateral triangle is√6, then find its area

1.	If the alltitude of an equilateral triangle is√6, then find its area
Answer» HI there! Your ANSWER :- 2√3 cm² $\bf\underline\blue{GIVEN :-}$ Altitude = √6 cm. Triangle is Equilateral. $\bf\underline\blue{SOLUTION :-}$ Use PYTHAGORAS Theorem. $\tt\red{{a}^{2} = {( \frac{a}{2} ) }^{2} + ( { \sqrt{6}) }^{2} }$ $\tt\green{{a}^{2} = \frac{{a}^{2}}{4} + 6}$ $\tt\pink{3 {a}^{2} = 24}$ $\tt\red{ {a}^{2} = 8}$ $\tt\gray{a = \sqrt{8} }$ Base = √8 cm. Height = √6 cm. Area = $\tt\purple{\dfrac{ \sqrt{8} \times \sqrt{6} }{2} }$ $\tt\orange{2 \sqrt{3} }$

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HI there!