Can anyone explain this question step by step
Find the area of the square using heron's forlula
class 9
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Can anyone explain this question step by step
Find the area of the square using heron's forlula
class 9
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In ∆ ABD
a = 100 cm
b = 160 cm
c = 100 cm
[tex] \tt{\color{olive}{S= {\dfrac{a+b+c}{2}}}} [/tex]
[tex] \tt {= {\dfrac{100+160+100}{2}} = {\dfrac{360}{2}} = 180} ~cm [/tex]
[tex] \tt{\color{navy}{A = \sqrt{S(S-a)(S-b)(S-c)}}} [/tex]
[tex] \tt{ = {\sqrt{180(180-100)(180-160)(180-100)}}} [/tex]
[tex] \tt{= {\sqrt{180(80)(20)(80)}}} ~ \tt{= {\sqrt{23040000}}} \\\\ {\fbox{\tt= {{4800~cm²}}}} [/tex]
Doing the same for ∆ CDB , we get the same area 4800 cm²
So , area of square = ∆ ABD + ∆ CDB
= 4800 + 4800
= 9600 cm²