Question

find the area of a triangle whose sides are 9cm 12cm and 15cm

Answer 1

36..........................m2

Answer 2

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

$\green{\therefore{\text{Area\:of\:triangle=54\:cm}^{2}}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Sides \: of \: triangle =9 cm,12 cm,15 cm} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Area \: of \: triangle = ?}$

• According to given question :

$\bold{As \: we \: know \: that \: herons \: formula} \\ : \implies s = \frac{a + b + c}{2} \\ \\ : \implies s = \frac{9+12+15}{2} \\ \\ : \implies s = \frac{36}{2} \\ \\ \green{ : \implies s =18 } \\ \\ \circ\: \bold{Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{18(18-9)(18-12)(18- 15)} \\ \\ : \implies \text{Area \: of \: triangle =}\sqrt{18\times 9\times6\times 3} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{2916} \\ \\ : \implies \text{Area \: of \: triangle =}54\: cm^{2} \\ \\ \ \green{\therefore \text{Area \: of \: triangle =54\: {cm}}^{2} }$