Question

using heron's formula find the area of an equilateral triangle whose perimeter is 15 CM

Answer 1

perimeter=15 cm,

3×side=15 cm,

side=5 cm,

therefore

Area of equilateral triangle=√3/4 × side²,

=√3/4 × 5²,

=25√3/4 cm²

Answer 2

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

$\green{\therefore{\text{Area\:of\:triangle=10.82\:cm}^{2}}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Perimter \: of \: triangle =15\:cm} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Area \: of \: triangle = ?}$

• According to given question :

$:\implies Perimeter\:of\:triangle=15\\\\ :\implies a+b+c=15\\\\ :\implies a+a+a=15\\\\ :\implies 3a=15\\\\ :\implies a=5\\\\\bold{As \: we \: know \: that \: herons \: formula} \\ : \implies s = \frac{a + b + c}{2} \\ \\ : \implies s = \frac{perimter\:of\:triangle}{2} \\ \\ : \implies s = \frac{15}{2} \\ \\ \green{ : \implies s =7.5 } \\ \\ \circ\: \bold{Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{7.5(7.5-5)(7.5-5)(7.5-5)}\\ \\ : \implies \text{Area \: of \: triangle =}\sqrt{7.5\times 2.5\times 2.5\times 2.5}\\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{117.1875} \\ \\ : \implies \text{Area \: of \: triangle =}10.82\: cm^{2} \\ \\ \ \green{\therefore \text{Area \: of \: triangle = 10.82\: {cm}}^{2} }$