Question

Can anyone explain this question step by step

Find the area of the square using heron's forlula

class 9

Answer 1

In ∆ ABD

a = 100 cm

b = 160 cm

c = 100 cm

$\tt{\color{olive}{S= {\dfrac{a+b+c}{2}}}}$

$\tt {= {\dfrac{100+160+100}{2}} = {\dfrac{360}{2}} = 180} ~cm$

$\tt{\color{navy}{A = \sqrt{S(S-a)(S-b)(S-c)}}}$

$\tt{ = {\sqrt{180(180-100)(180-160)(180-100)}}}$

$\tt{= {\sqrt{180(80)(20)(80)}}} ~ \tt{= {\sqrt{23040000}}} \\\\ {\fbox{\tt= {{4800~cm²}}}}$

Doing the same for ∆ CDB , we get the same area 4800 cm²

So , area of square = ∆ ABD + ∆ CDB

= 4800 + 4800

= 9600 cm²