Question

Find the area of an equilateral triangle whose one side is 5cm

Answer 1

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Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\therefore{\text{Area\:of\:triangle=10.82\:cm}^{2}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{ \underline \bold{Given : }} \\ : \implies \text{Sides \: of \: triangle =5 cm,5 cm,5 cm} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Area \: of \: triangle = ?}$

• According to given question :

$\bold{As \: we \: know \: that \: herons \: formula} \\ : \implies s = \frac{a + b + c}{2} \\ \\ : \implies s = \frac{5+5+5}{2} \\ \\ : \implies s = \frac{15}{2} \\ \\ \green{ : \implies s =7.5 } \\ \\ \circ\: \bold{Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{7.5(7.5- 5)(7.5-5)(7.5- 5)} \\ \\ : \implies \text{Area \: of \: triangle =}\sqrt{7.5\times 2.5\times 2.5\times 2.5} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{117.1875} \\ \\ : \implies \text{Area \: of \: triangle =}10.82\: cm^{2} \\ \\ \ \green{\therefore \text{Area \: of \: triangle =10.82\: {cm}}^{2} }$

$\bold{Another \: method} \\ : \implies \text{Area \: of \: equilateral \: triangle =} \frac{ \sqrt{3} }{4} {side}^{2} \\ \\ : \implies \text{Area \: of \: equilateral \: triangle =} \frac{ \sqrt{3} }{4} \times {5}^{2} \\ \\ : \implies \text{Area \: of \: equilateral \: triangle =} \frac{ \sqrt{3} \times 25}{4} \\ \\ : \implies \text{Area \: of \: equilateral \: triangle =} {1.732 \times 6.25} \\ \\ \green{: \implies \text{Area \: of \: equilateral \: triangle =}10.82 {cm}^{2} }$