Premium Online Home Tutors
3 Tutor System
Starting just at 265/hour
Answer :
Let each side of the triangle be a cm. Then,
Area = 17320.5 cm2
\( \Rightarrow \ \frac{ \sqrt{3}}{4}a^2 \ = \ 17320.5 \)
[\(\therefore \) Area \(= \ \frac{ \sqrt{3}}{4}(side)^2 \)]
\( \Rightarrow \ a^2 \ = \ \frac{17320.5 \ × \ 4}{ \sqrt{3}} \) \( = \ 40000 \)
\( \Rightarrow \ a \ = \ 200 \)
\(\therefore \) Radius of each circle = \( \frac{a}{2} = 100 cm.\)
Now, required area = Area of \(\triangle \) ABC - 3 × (Area of a sector of angle 60º in a circle of 100 cm)
\( = \ 17320.5 \ - \ 3( \frac{60}{360} \ × \ 3.14 \ × \ 100 \ × \ 100) \)
\( = \ 17320.5 \ - \ 15700 \ = \ 1620.5 \) cm2