Question

using heron's formula find the area of equilateral triangle whose perimeter is 28 CM

Answer 1

area of triangle =side×side ×side
=28×28×28
=21952 cm

Answer 2

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

$\green{\therefore{\text{Area\:of\:triangle=37.72\:cm}^{2}}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Perimter \: of \: triangle =28\:cm} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Area \: of \: triangle = ?}$

• According to given question :

$:\implies Perimeter\:of\:triangle=28\\\\ :\implies a+b+c=28\\\\ :\implies a+a+a=28\\\\ :\implies 3a=28\\\\ :\implies a=\frac{28}{3}\\\\\bold{As \: we \: know \: that \: herons \: formula} \\ : \implies s = \frac{a + b + c}{2} \\ \\ : \implies s = \frac{perimter\:of\:triangle}{2} \\ \\ : \implies s = \frac{28}{2} \\ \\ \green{ : \implies s =14 } \\ \\ \circ\: \bold{Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{14(14-\frac{28}{3})(14-\frac{28}{3})(14- \frac{28}{3})} \\ \\ : \implies \text{Area \: of \: triangle =}\sqrt{\frac{14\times 14\times 14\times 14 }{27}} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{\frac{38416}{27}} \\ \\ : \implies \text{Area \: of \: triangle =}37.72\: cm^{2} \\ \\ \ \green{\therefore \text{Area \: of \: triangle = 37.72\: {cm}}^{2} }$