Question

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

Answer 1

sp=a+b+c/2
10+10+12/2=32/2=16
a=√s(s-a)(s-b) (s-c)
√16(16-10)(16-10)(16-12)
=√16*6*6*4
=4*6*2
=48cm.sq

Answer 2

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

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

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

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

• According to given question :

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