Mathematics Question and Solution

By Ogheneovo Daniel Ephivbotor
6th April, 2024

Let the inscribed bigger quarter circle radius be a.


Let the inscribed big quarter circle radius be b.


c = 5 cm.

c is the radius of the inscribed semi circle.


It implies;


a+b = 10 --- (1).


a+5 =√(10²+5²)

a = √(125)-5

a = 5(√(5)-1) cm.

Again, a is the inscribed bigger quarter circle radius.


And;


a+b = 10

b = 10-a

b = 10-5(√(5)-1)

b = (15-5√(5)) cm.

Again, b is the inscribed big quarter circle radius.


Area Blue is;


= (10*10)-½(5²)π-¼(5√(5)-5)²π-¼(15-5√(5))²π

= 100-½(25π)-¼(125-50√(5)+25)π-¼(225-150√(5)+125)π

= 100-½(25π)-¼(150-50√(5))π-¼(350-150√(5))π

= ¼(400-50π-150π+50√(5)π-350π+150√(5)π)

= ¼(400-550π+200√(5)π)

= ½(200-275π+100√(5)π)

= 19.2717466834 cm²

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