Question

Each side of an equilateral triangle is 8cm, its area is _____ .
$(a)16 \sqrt{3 {cm}^{2} }$
$(b)8 \sqrt{3} {cm}^{2}$
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Answer 1

EXPLANATION.

Each side of an equilateral triangle = 8 cm.

As we know that,

Formula of :

Area of an equilateral triangle = (√3)/(4) x (a²).

Using this formula in the equation, we get.

Side = a = 8 cm.

Area of an equilateral triangle = (√3)/(4) x (8)².

Area of an equilateral triangle = (√3)/(4) x 64.

Area of an equilateral triangle = (√3) x 16.

Area of an equilateral triangle = 16√3 cm².

Option [A] is correct answer.

Answer 2

$\rm \bigstar \: Given :$

$\rm \: Each \: side \: of \: an \: \: equilateral \: triangle \: is \: 8cm$

$\rm \bigstar \: To \: Find :$

$\rm \: Area \: of \: that \: equilateral \: triangle$

$\rm \bigstar \: Solution :$

$\rm \: The \: formula \: to \: calculate \: the \: area \: of \: an$

$\rm \: equilateral \: triangle \: is \: \: given \: as \: , Area \: of \: an$

$\rm \: equilateral \: triangle.$

$\rm \implies \:A = \dfrac{ \sqrt{3} }{4} \: {a}^{2} \: square \: units.$

$\rm \: Where$

$\rm \: A \implies \: Area \: of \: Equilateral \: triangle$

$\rm \: a \implies \: Side \: length$

$\rm \: By \: using \: this \: formula$

$\rm \implies \: \dfrac{ \sqrt{3} }{4} \times {8}^{2}$

$\rm \implies \: \dfrac{ \sqrt{3} }{4} \times 64$

$\rm \implies \: \dfrac{ \sqrt{3} }{ \cancel{4}}\times \: \cancel{ {64}}^{ \: 16}$

$\rm \implies \: 16 \: \sqrt{3} \: {cm}^{2}$

$\rm \: Therefore$

$\rm \implies \:(a) \: \: 16 \: \sqrt{3} \: {cm}^{2} \: is \: correct \: option$