Question

Find the area of a triangle if its sides are 100cm, 100cm and125cm using herons formula

Answer 1

Step 1: Find the semi perimeter:
(100 + 100 + 125) / 2 = 162.5

Step 2: Use the formula ($\sqrt{s (s-a) (s-b) (s-c)}$):
$\sqrt{162.5(62.5)(62.5)(37.5}$ = 4879

Answer 2

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

$\green{\therefore{\text{Area\:of\:triangle=4878.9\:cm}^{2}}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Sides \: of \: triangle = 100 cm,100 cm,125 cm} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Area \: of \: triangle = ?}$

• According to given question :

$\bold{As \: we \: know \: that \: herons \: formula} \\ : \implies s = \frac{a + b + c}{2} \\ \\ : \implies s = \frac{100+100+ 125}{2} \\ \\ : \implies s = \frac{325}{2} \\ \\ \green{ : \implies s = 162.5} \\ \\ \circ\: \bold{Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{162.5(162.5- 100)(162.5-100)(162.5- 125)} \\ \\ : \implies \text{Area \: of \: triangle =}\sqrt{162.5\times 62.5 \times 62.5\times 37.5} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{23803710.9375} \\ \\ : \implies \text{Area \: of \: triangle =}4878.9\: cm^{2} \\ \\ \ \green{\therefore \text{Area \: of \: triangle = 4878.9\:{cm}}^{2} }$