# What is the ratio of area colored as red and area colored as blue?

+1 vote
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What is the ratio of area colored as red and area colored as blue?

posted Jul 2, 2015

+1 vote

blue area=0.25*d^2-(3.14/16)*d^2=0.05375*d^2
red area=(3.14/16)*d^2=0.19625*d^2
thus red area:blue area=0.19625:0.05375=3.651163:1

+1 vote

Let's 'd' is
dia of circle=side of the square.

Area of blue=area of square - area of circle
=d^2-pi/4d^2..... (i)
Area of red =pi/4 d^2.... (ii)

Ratio of area of red/area of blue is
=(ii) /(i)

Pi/4 d ^2
=----------------
d^2-pi/4 d^2

Pi/4
=-------- (by removing d^2)
1-pi/4

=22/6 (by putting the value of pi =22/7)

So ratio is 22 to 6

ie 22:6 or 3.6666666666.... :1

let the radius of circle is 2r. then area of one of the four block of circle is Pi * r^2 ,now area of the blue region is: area of one of the fourth triangle - area of one of the fourth block of circle = (4 * r^2) - (Pi * r^2)= r^2*(4-Pi)
ratio= Pi/(4-Pie)

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