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Geometry Level 4

The area of an equilateral triangle is 17320.5 cm 2 ^2 .About each angular point as centre, a circle is described with radius equal to half the length of the side of the triangle.Find the area of the triangle not included the circle.( π = 3.14 \pi=3.14 )


The answer is 1620.5.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

The three circular sectors, each of 60 degrees, with radius half the triangle side, eat up an area . Let A=given area.
( H a l f t h e t r i a n g l e s i d e ) 2 = ( 1 2 ) 2 ∗ 4 3 ∗ A = r 2 . A r e a l e f t = A { 1 − 3 ∗ π r 2 ∗ 60 360 } = A ( 1 − 1.4 2 3 ) R e q u i r e d a r e a = 1620.51. ( Half ~the~ triangle~ side)^2= (\dfrac 1 2)^2*\dfrac 4{ \sqrt3}*A=r^2.\\ Area~left=A\{1- 3*\dfrac{\pi r^2*60}{360} \}=A(1-\dfrac{1.4}{2\sqrt3})\\ Required ~area=\Large ~~~~~~~\color{#D61F06}{1620.51}.

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