Question

Use a fórmula de Heron para encontrar a área de um triângulo equilátero de lado L.

Answer 1

Resposta:

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Answer 2

Resposta:

$A=\frac{L\sqrt{3} }{2}$

Explicação passo a passo:

$A=\sqrt{p(p-a)(p-b)p-c)} ,~~onde~~p=\frac{a+b+c}{2} \\\\p=\frac{L+L+L}{2}\\\\p=\frac{3L}{2} \\\\A=\sqrt{\frac{3L}{2}(\frac{3L}{2}-L)^3 }\\\\A=\sqrt{\frac{3L}{2}*\frac{L}{2} }\\\\A=\sqrt{\frac{3L^2}{4} } \\\\A=\frac{L\sqrt{3} }{2}$