Mathematics Question and Solution
Calculating the red shaded area.
Notice.
10 cm is the radius of each of the four equal inscribed circles.
tana = 10/(4*10)
a = atan(¼)°
a = 14.0362434679°
b = 3*10
b = 30 cm.
(10/sin14.0362434679) = (30/sinc)
c = 133.313856658°
d = 180-a-c
d = 180-14.0362434679-133.313856658
d = 32.6498998741°
e = 90-d
e = 90-32.6498998741
e = 57.3501001259°
f = 180-2a
f = 180-2*14.0362434679
f = 151.927513064°
Therefore, the required red shaded area is;
Area rectangle with length 30 cm and width 10 cm - Area triangle with height 30 cm and base 10sin32.6498998741 cm - Area sector with radius 10 cm and angle 57.3501001259° - Area sector with radius 10 cm and angle 151.927513064° + Area triangle with height 10 cm and base 10sin151.927513064 cm - Area square with side 10 cm + Area quarter circle with radius 10 cm.
= (30*10)-(0.5*30*10sin32.6498998741)-(57.3501001259π*10²/360)-(151.927513064π*10²/360)+(0.5*10²sin151.927513064)-(10*10)+(0.25*π*10²)
= 300-80.9256430176-50.0474036773-132.581766367+23.5294117648-100+78.5398163397
= 38.5144150426 cm²
