The area of an equilateral triangle with a side of 12 cm is:


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Answer:

^@ 36\sqrt{ 3} ^@ cm2

Step by Step Explanation:
  1. As per Heron's formula, the area of a triangle with sides a, b and c and perimeter 2S = ^@ \sqrt{ S(S-a)(S-b)(S-c) } ^@
  2. Here, a = b = c = 12 and S =  
    3
    2
      × a = 18.
  3. Therefore, Area = ^@\sqrt{ 18 \times (18 - 12) \times (18 - 12) \times (18 - 12) }^@
    ⇒ Area = ^@\sqrt{ (18 \times 6 \times 6 \times 6) }^@
    ⇒ Area = ^@ 36\sqrt{ 3} ^@ cm2

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