Question

Using herons formula .find the area of an equilateral triangle shoes perimeter is 24 cm

Answer 1

Answer:

Step-by-step explanation:

Answer 2

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

$\green{\therefore{\text{Area\:of\:triangle=27.71\:cm}^{2}}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Perimter \: of \: triangle =24\:cm} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Area \: of \: triangle = ?}$

• According to given question :

$:\implies Perimeter\:of\:triangle=24\\\\ :\implies a+b+c=24\\\\ :\implies a+a+a=24\\\\ :\implies 3a=24\\\\ :\implies a=8\\\\\bold{As \: we \: know \: that \: herons \: formula} \\ : \implies s = \frac{a + b + c}{2} \\ \\ : \implies s = \frac{perimter\:of\:triangle}{2} \\ \\ : \implies s = \frac{24}{2} \\ \\ \green{ : \implies s =12 } \\ \\ \circ\: \bold{Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{12(12-8)(12-8)(12-8) }\\ \\ : \implies \text{Area \: of \: triangle =}\sqrt{12\times 4\times 4\times 4} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{768} \\ \\ : \implies \text{Area \: of \: triangle =}27.71\: cm^{2} \\ \\ \ \green{\therefore \text{Area \: of \: triangle =27.71\: {cm}}^{2} }$