Question

sides of triangle are 13 15 17 cm find the area of a triangle using heron's formula​

Answer 1

Answer:

First of all, we will find S=a+b+c/2

(13+15+17)/2

45/2

Now, by heron's formula,

=√S(s-a) (s-b) (s-c)

=√22.5(22.5-13)(22.5-15)(22.5-17)

=√22.5 x 9.5 x 7.5 x 5.5

=√8817.18

=93.90 sq cm(approx)

Answer 2

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

$\green{\therefore{\text{Area\:of\:triangle=93.9\:cm}^{2}}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Sides \: of \: triangle =13 cm,15 cm,17 cm} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Area \: of \: triangle = ?}$

• According to given question :

$\bold{As \: we \: know \: that \: herons \: formula} \\ : \implies s = \frac{a + b + c}{2} \\ \\ : \implies s = \frac{13+15+ 17}{2} \\ \\ : \implies s = \frac{45}{2} \\ \\ \green{ : \implies s =22.5} \\ \\ \circ\: \bold{Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{22.5(22.5- 13)(22.5-15)(22.5- 17)} \\ \\ : \implies \text{Area \: of \: triangle =}\sqrt{22.5\times 9.5\times 7.5\times 5.5} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{8817.1875} \\ \\ : \implies \text{Area \: of \: triangle =}93.9\: cm^{2} \\ \\ \ \green{\therefore \text{Area \: of \: triangle = 93.9\: {cm}}^{2} }$