SOLUTION: please help me solve this equation ; the circle is divided into 4 parts a,b,c,d where part a & c form a semicircle and part b&d form the other semicircle area of part a to area of

Question 746229: please help me solve this equation ; the circle is divided into 4 parts a,b,c,d where part a & c form a semicircle and part b&d form the other semicircle area of part a to area of part c is in the ratio 1: 3 the area of part b to the area of part d is in the ratio 1:2. the area of part c is bigger than part b by 20 SquareCentimeters find the area of the whole cirle
Answer by savvyhush23(50) (Show Source): You can put this solution on YOUR website!
please help me solve this equation ; the circle is divided into 4 parts a,b,c,d where part a & c form a semicircle and part b&d form the other semicircle area of part a to area of part c is in the ratio 1: 3 the area of part b to the area of part d is in the ratio 1:2. the area of part c is bigger than part b by 20 SquareCentimeters find the area of the whole cirle.
.
.
Ok, let solve it one by one,
Let,
At = Total area of circle
Aa = Area of a
Ab = Area of b
Ac = Area of c
Ad = Area of d
.
.
part a & c form a semicircle...part b&d form the other semicircle:
, and
part a to area of part c is in the ratio 1:3..., or
part b to the area of part d is in the ratio 1:2..., or
the area of part c is bigger than part b by 20...
.
.
Ok, here is my favorite part:
We have 5 unknown (At, Aa, Ab, Ac, and Ad), so we have to form 5 equations to solve it. The 4 equations are ready above,
.
.
since a & c and b & d are semi circle, , equation 5
we have the 2 equations for that above, substituting here, , or , then add this to the other 3 remaining equation:
.
.
but and , so, ,
So, , , , and
.
.
Therefore,
Check it, the value of individual area must satisfy the given ratio.
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