Question

Find the area of an equilateral triangle of side a using Heron formula

Answer 1

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

$\green{\therefore{\text{Area\:of\:triangle=0.433a}^{2}\:cm^{2}}}$

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

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

• According to given question :

$\bold{As \: we \: know \: that \: herons \: formula} \\ : \implies s = \frac{a + b + c}{2} \\ \\ : \implies s = \frac{a+a+ a}{2} \\ \\ : \implies s = \frac{3a}{2} \\ \\ \green{ : \implies s = 1.5a} \\ \\ \circ\: \bold{Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{1.5a(1.5a- a)(1.5a-a)(1.5a- a)} \\ \\ : \implies \text{Area \: of \: triangle =}\sqrt{1.5a\times 0.5a\times 0.5a\times 0.5a} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{0.1875a^{4}} \\ \\ : \implies \text{Area \: of \: triangle =}0.433a^{2}\: cm^{2} \\ \\ \ \green{\therefore \text{Area \: of \: triangle = 0.433a}^{2}\: {cm}^{2} }$