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Question Number 72997 by yannickmendes_33 last updated on 05/Nov/19

T h e a r e a o f t h e e q u i l a t e r a l t r i a n g l e i s e q u a l t o \frac{\sqrt{16} \sqrt{8}}{3 \sqrt{π}}

C a l c u l a t e t h e a r e a o f t h e c i r c l e i n s c r i b e d i n t h e t r i a n g l e .

Answered by Kunal12588 last updated on 05/Nov/19

a r e a o f e q u i l a t e r a l △ = \frac{\sqrt{3} a^{2}}{4} = \frac{\sqrt{16} \sqrt{8}}{3 \sqrt{π}} = \frac{8 \sqrt{2}}{3 \sqrt{π}}

\Rightarrow \frac{a^{2}}{4} = \frac{8 \sqrt{2}}{3 \sqrt{3 π}}

a r e a o f c i r c l e = π r^{2}

\frac{h_{1}}{h_{2}} = \frac{2}{1}

\Rightarrow h_{1} = 2 h_{2}

h_{1} + h_{2} = h

\Rightarrow 3 h_{2} = h

\Rightarrow h_{2} = \frac{h}{3}

h_{2} = r = \frac{h}{3}

a r c i r c l e = π r^{2}

= π {(\frac{h}{3})}^{2}

= π {(\frac{1}{3} \times \frac{a \sqrt{3}}{2})}^{2}

= π \times \frac{1}{3} \times \frac{a^{2}}{4}

= π \times \frac{1}{3} \times \frac{8 \sqrt{2}}{3 \sqrt{3 π}}

= \frac{8 \sqrt{6 π}}{27}