Question

Using heron's formula find the area of a triangle whose sides are 5cm 12cm and 13cm

Answer 1

let sides of ∆ be
a = 5
b = 12
c = 13
s = (a+b+c)/2 = (5+12+13)/2 = 15

heron's formula
area = √(s(s-a)(s-b)(s-c))

= √(15(15-5)(15-12)(15-13))

= √(15*10*3*2). =√900 = 30

thus area of ∆ = 30 cm²

Answer 2

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

$\green{\therefore{\text{Area\:of\:triangle=30\:cm}^{2}}}$

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

$\green{ \underline \bold{Given : }} \\ : \implies \text{Sides \: of \: triangle = 5 cm,12 cm,13 cm} \\ \\ \red{ \underline \bold{To \: Find : }} \\ : \implies \text{Area \: of \: triangle = ?}$

• According to given question :

$\bold{As \: we \: know \: that \: herons \: formula} \\ : \implies s = \frac{a + b + c}{2} \\ \\ : \implies s = \frac{5+ 12+ 13}{2} \\ \\ : \implies s = \frac{30}{2} \\ \\ \green{ : \implies s = 15} \\ \\ \circ\: \bold{Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{15(15- 5)(15-12)(15- 13)} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{15 \times 10\times 3\times 2} \\ \\ : \implies \text{Area \: of \: triangle =} \sqrt{900} \\ \\ : \implies \text{Area \: of \: triangle =}30\: cm^{2} \\ \\ \ \green{\therefore \text{Area \: of \: triangle =30{cm}}^{2} }$