Question

find the area of the triangle whose sides have 12cm, 6cm, 15cm, using Heron's formula

Answer 1

Here is the answer to your questions

Answer 2

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

$\green{\therefore{\text{Area\:of\:triangle=34.19\:cm}^{2}}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Sides \: of \: triangle = 12 cm,6 cm,15 cm} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Area \: of \: triangle = ?}$

• According to given question :

$\bold{As \: we \: know \: that \: herons \: formula} \\ : \implies s = \frac{a + b + c}{2} \\ \\ : \implies s = \frac{12+ 6+ 15}{2} \\ \\ : \implies s = \frac{33}{2} \\ \\ \green{ : \implies s = 16.5} \\ \\ \circ\: \bold{Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{16.5(16.5- 12)(16.5-6)(16.5- 15)} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{16.5 \times 4.5\times 10.5\times 1.5} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{1169.43475} \\ \\ : \implies \text{Area \: of \: triangle =}34.19\: cm^{2} \\ \\ \ \green{\therefore \text{Area \: of \: triangle = 34.19 {cm}}^{2} }$