Question

perimeter of an equilateral triangle is 36cm.Find it's area using Herons formula​

Answer 1

Answer:

Step-by-step explanation:

perimeter = 36

one side = 36/3=12

area = root3/4*side

area=3*root3

Answer 2

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

$\green{\therefore{\text{Area\:of\:triangle=62.35\:cm}^{2}}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Perimter \: of \: triangle =36\:cm} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Area \: of \: triangle = ?}$

• According to given question :

$:\implies Perimeter\:of\:triangle=36\\\\ :\implies a+b+c=36\\\\ :\implies a+a+a=36\\\\ :\implies 3a=36\\\\ :\implies a=12\\\\\bold{As \: we \: know \: that \: herons \: formula} \\ : \implies s = \frac{a + b + c}{2} \\ \\ : \implies s = \frac{perimter\:of\:triangle}{2} \\ \\ : \implies s = \frac{36}{2} \\ \\ \green{ : \implies s =18 } \\ \\ \circ\: \bold{Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{18(18-12)(18-12)(18-12) }\\ \\ : \implies \text{Area \: of \: triangle =}\sqrt{18\times 6\times 6\times 6} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{3888} \\ \\ : \implies \text{Area \: of \: triangle =}62.35\: cm^{2} \\ \\ \ \green{\therefore \text{Area \: of \: triangle =62.35\: {cm}}^{2} }$