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Question

Prove that the area of an equilateral triangle of side a is 34a2.

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Solution

ABC is equilateral triangle:-
In an equilateral triangle median =altitude
ADBC and BD=DC=BC2=a2
Consider triangle ABD
sinABD=ADAB
32=ADa
AD=3a2
area of triangle ABC 1/2×box×height
1/2×(BC)×(AD)
12(a)(32a)
area of triangle ABC 32a2
are of equilateral triangle is 3a24

1370512_1171351_ans_29561ab40d3441c0bea363ff31e1f062.png

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