Question

Find the area of triangle whose sides are length 10cm 14cm and 16cm using heron's formula

Answer 1

hope the answer is correct

Answer 2

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

$\green{\therefore{\text{Area\:of\:triangle=69.28\:cm}^{2}}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Sides \: of \: triangle = 10 cm,14 cm,16 cm} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Area \: of \: triangle = ?}$

• According to given question :

$\bold{As \: we \: know \: that \: herons \: formula} \\ : \implies s = \frac{a + b + c}{2} \\ \\ : \implies s = \frac{10+ 14+ 16}{2} \\ \\ : \implies s = \frac{40}{2} \\ \\ \green{ : \implies s = 20} \\ \\ \circ\: \bold{Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{20(20- 10)(20-14)(20-16)} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{20\times 10\times 6\times 4} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{4800} \\ \\ : \implies \text{Area \: of \: triangle =}69.28\: cm^{2} \\ \\ \ \green{\therefore \text{Area \: of \: triangle = 69.28 {cm}}^{2} }$