Question

Find find the area of equilateral triangle whose side is 4cm

Answer 1

6.93cm2 is the right answer

Answer 2

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

$\green{\therefore{\text{Area\:of\:triangle=6.92\:cm}^{2}}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Sides \: of \: triangle =4 cm,4 cm,4 cm} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Area \: of \: triangle = ?}$

• According to given question :

$\bold{As \: we \: know \: that \: herons \: formula} \\ : \implies s = \frac{a + b + c}{2} \\ \\ : \implies s = \frac{4+4+4}{2} \\ \\ : \implies s = \frac{12}{2} \\ \\ \green{ : \implies s =6 } \\ \\ \circ\: \bold{Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{6(6- 4)(6-4)(6- 4)} \\ \\ : \implies \text{Area \: of \: triangle =}\sqrt{6\times 2\times 2\times 2} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{48} \\ \\ : \implies \text{Area \: of \: triangle =}6.92\: cm^{2} \\ \\ \ \green{\therefore \text{Area \: of \: triangle =6.92\: {cm}}^{2} }$

$\bold{Another \: method} \\ : \implies \text{Area \: of \: equilateral \: triangle =} \frac{ \sqrt{3} }{4} {side}^{2} \\ \\ : \implies \text{Area \: of \: equilateral \: triangle =} \frac{ \sqrt{3} }{4} \times {4}^{2} \\ \\ : \implies \text{Area \: of \: equilateral \: triangle =} \frac{ \sqrt{3} \times 16}{4} \\ \\ : \implies \text{Area \: of \: equilateral \: triangle =} {1.732 \times 4} \\ \\ \green{: \implies \text{Area \: of \: equilateral \: triangle =}6.92 {cm}^{2} }$