Question

find the area of a triangle,whose sides are 5,11,13. by using herons formula

Answer 1

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Answer 2

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

$\green{\therefore{\text{Area\:of\:triangle=26.89\:cm}^{2}}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Sides \: of \: triangle = 5,11,13} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Area \: of \: triangle = ?}$

• According to given question :

$\bold{As \: we \: know \: that \: herons \: formula} \\ : \implies s = \frac{a + b + c}{2} \\ \\ : \implies s = \frac{5 + 11 + 13}{2} \\ \\ : \implies s = \frac{29}{2} \\ \\ \green{ : \implies s = 14.5} \\ \\ \circ\: \bold{area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{14.5(14.5 - 5)(14.5 - 11)(14.5 - 13)} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{14.5 \times 9.5 \times 3.5 \times 1.5} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{723.1875} \\ \\ : \implies \text{Area \: of \: triangle =}26.89 \: cm^{2} \\ \\ \ \green{\therefore \text{Area \: of \: triangle = 26.89 {cm}}^{2} }$