Question

calculate the area of shaded portion...........
AB=120m
AC=122m
BC=22m
BO=24m
CO=26m

I have attached the figure...................

Answer 1

$\huge {\boxed {\mathfrak\pink {\fcolorbox {red}{yellow}{Answer}}}}$

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Given❇

AB=120m

AC=122m

BC=22m

BO=24m

CO=26m

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Find❇

Area of the shaded portion = ?

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Solution❇

Area of triangle ABC,

Using Heron's formula,

S=$\frac {AB+BC+AC}{2}$

S=$\frac {120+122+22}{2}$

S=$\frac {264}{2}$

S= 132

=$\sqrt {S(S-AB)(S-AC)(S-BC)}$

=$\sqrt {132(132-120)(132-122)(132-22)}$

=$\sqrt {132(12)(10)(110)}$

=$\sqrt {1742400}$

=${1320m}^{2}$

Area of triangle BOC

Using Heron's formula,

S=$\frac {BO+BC+OC}{2}$

S=$\frac {24+22+26}{2}$

S=$\frac {72}{2}$

S=36

=$\sqrt {S(S-AB)(S-AC)(S-BC)}$

=$\sqrt {36(36-24)(36-22)(36-26)}$

=$\sqrt {36(12)(14)(10)}$

=$\sqrt {60480}$

= 245.92

Area of the shaded portion ,

= ABC - BOC

= 1320 - 245.92

= =${1074.08m}^{2}$

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