Question

Find the area of triangle whose lengths of sides are 15m,17m,21m by using heron's formula

Answer 1

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Answer 2

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

$\green{\therefore{\text{Area\:of\:triangle=126.18\:cm}^{2}}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Sides \: of \: triangle = 15 cm,17 cm,21 cm} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Area \: of \: triangle = ?}$

• According to given question :

$\bold{As \: we \: know \: that \: herons \: formula} \\ : \implies s = \frac{a + b + c}{2} \\ \\ : \implies s = \frac{15+ 17+ 21}{2} \\ \\ : \implies s = \frac{53}{2} \\ \\ \green{ : \implies s = 26.5} \\ \\ \circ\: \bold{Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{26.5(26.5- 15)(26.5-17)(26.5- 21)} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{26.5 \times 11.5\times 9.5\times 5.5} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{15923.1875} \\ \\ : \implies \text{Area \: of \: triangle =}126.18\: cm^{2} \\ \\ \ \green{\therefore \text{Area \: of \: triangle = 126.18 {cm}}^{2} }$