Question

find the area of triangle 50,78, 112 using herons formula

Answer 1

Hii ☺ !!


Let , First side ( A ) = 50


Second side ( B ) = 78


And,


Third side ( C ) = 112



Therefore,



Semi Perimeter ( S ) = A + B + C /2 = ( 50+78+112)/2 = 240/2 = 120 .







( S - A ) = 120 - 50 = 70


( S - B ) = 120 - 78 = 42


( S - C ) = 120 - 112 = 8



Therefore,


Area of triangle = √s ( S - A ) ( S - B )(S - C )




=> √120 × 70 × 42 × 8



=> √2822400 = 1680 square units.

Answer 2

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

$\green{\therefore{\text{Area\:of\:triangle=1680\:cm}^{2}}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Sides \: of \: triangle =50 cm,78 cm,112 cm} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Area \: of \: triangle = ?}$

• According to given question :

$\bold{As \: we \: know \: that \: herons \: formula} \\ : \implies s = \frac{a + b + c}{2} \\ \\ : \implies s = \frac{50+78+ 112}{2} \\ \\ : \implies s = \frac{240}{2} \\ \\ \green{ : \implies s =120 } \\ \\ \circ\: \bold{Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{120(120- 50)(120-78)(120- 112)} \\ \\ : \implies \text{Area \: of \: triangle =}\sqrt{120\times 70\times 42\times 8} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{2822400} \\ \\ : \implies \text{Area \: of \: triangle =}1680\: cm^{2} \\ \\ \ \green{\therefore \text{Area \: of \: triangle = 1680\: {cm}}^{2} }$