Mathematics Question and Solution
a² = 2*6²
a² = 2*36
a = √(2*36)
a= 6√(2) units.
Let the radius of the small inscribed circle be r.
Calculating r.
b² =2r²
b = √(2)r units.
It implies;
b+r+6 = a
√(2)r+r+6 = 6√(2)
(√(2)+1)r = 6√(2)-6
r = (6√(2)-6)/(√(2)+1)
r = (12-6√(2)-6√(2)+6)/1
r = (18-12√(6))
r = 6(3-2√(2) units.
r = 1.0294372515 units.
It implies;
Area green is;
Half area square with side 6 units - Area sector with radius 6 units and angle 45° - Half area square with side 1.0294372515 units - Area sector with radius 1.0294372515 units and angle 135°
= ½(6*6)-(45π*6*6/360)-½(1.0294372515*1.0294372515)-(135π*1.0294372515*1.0294372515/360)
= 18-14.1371669412-0.5298705274-1.2484780171
= 2.0844845143 square units.
