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

Answer:

$36\sqrt{ 3}$ cm²

Step by Step Explanation:

As per Heron's formula, the area of a triangle with sides a, b and c and perimeter 2S = $\sqrt{ S(S-a)(S-b)(S-c) }$
Here, a = b = c = 12 and S =
3
2
× a = 18.
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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