find the area of a triangle whose sides are 10cm,10cm and 12cm by using herons formula. Created by harman90. Math

find the area of a triangle whose sides are 10cm,10cm and 12cm by using herons f...

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

$\green{\therefore{\text{Area\:of\:triangle=48\:cm}^{2}}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Sides \: of \: triangle = 10 cm,10 cm,12 cm} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Area \: of \: triangle = ?}$

• According to given question :

$\bold{As \: we \: know \: that \: herons \: formula} \\ : \implies s = \frac{a + b + c}{2} \\ \\ : \implies s = \frac{10+ 10+ 12}{2} \\ \\ : \implies s = \frac{32}{2} \\ \\ \green{ : \implies s = 16} \\ \\ \circ\: \bold{area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{16(16- 10)(16-10)(16- 12)} \\ \\ : \implies \text{Area \: of \: triangle =}\sqrt{16 \times 6 \times 6\times 4} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{2304} \\ \\ : \implies \text{Area \: of \: triangle =}48 \: cm^{2} \\ \\ \ \green{\therefore \text{Area \: of \: triangle = 48 {cm}}^{2} }$

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