Question

Find the area of the triangle in herons formula if the sides are 8m,9m,13m

Answer 1

s=(8+9+13)/2=15m

a=√15(15-8)(15-9)(15-13)

a=√15*7*6*2

a=√3*5*3*2*2*7

taking out pairs,

a=3*2√5*7

a=6√35 m^2

Answer 2

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

$\green{\therefore{\text{Area\:of\:triangle=35.5\:m}^{2}}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Sides \: of \: triangle = 8 m,9 m,13 m} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Area \: of \: triangle = ?}$

• According to given question :

$\bold{As \: we \: know \: that \: herons \: formula} \\ : \implies s = \frac{a + b + c}{2} \\ \\ : \implies s = \frac{8+ 9+ 13}{2} \\ \\ : \implies s = \frac{30}{2} \\ \\ \green{ : \implies s = 15} \\ \\ \circ\: \bold{Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{15(15- 8)(15-9)(15- 13)} \\ \\ : \implies \text{Area \: of \: triangle =}\sqrt{15\times 7 \times 6\times 2} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{1260} \\ \\ : \implies \text{Area \: of \: triangle =}35.5\: m^{2} \\ \\ \ \green{\therefore \text{Area \: of \: triangle = 35.5 {m}}^{2} }$