Question

find the area of the equilateral triangle whose perimeter is 18cm using heron's formula​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

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

$\green{\therefore{\text{Area\:of\:triangle=15.58\:cm}^{2}}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Perimeter\: of \: triangle = 18} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Area \: of \: triangle = ?}$

• According to given question :

$:\implies Perimeter\:of\:triangle=18\\\\ :\implies a+b+c=18\\\\ :\implies 3a=18\\\\ :\implies a=6\:cm\bold{As \: we \: know \: that \: herons \: formula} \\\\ : \implies s = \frac{a + b + c}{2} \\ \\ : \implies s = \frac{Perimeter}{2} \\ \\ : \implies s = \frac{18}{2} \\ \\ \green{ : \implies s = 9} \\ \\ \circ\: \bold{area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{9(9-6)(9-6)(9- 6)} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{9 \times 3\times 3\times 3} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{243} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =15.58 \: cm^{2} \\ \\ \ \green{\therefore \text{Area \: of \: triangle = 15.58 {cm}}^{2} }$