Mathematics Question and Solution
Calculating Area Green.
Notice.
The composite plane shape is drawn to scale.
a = 6 cm.
Let b = x cm.
b is the width of the inscribed rectangle.
c = 2x cm.
c is the length of the inscribed rectangle.
d² = x²+(½(x))²
d² = x²+¼(x)²
d = √(¼(5x²))
d = ½√(5)x cm.
d is the radius of the circle.
e = 2d
e = 2*½√(5)x
e = √(5)x cm.
e is the diameter of the circle.
Calculating x.
2x ~ 6
√(5)x ~ ½√(5)x
Cross Multiply.
√(5)x² = 6√(5)x
√(5)x = 6√(5)
x = 6 cm.
Again, x is the width of the inscribed rectangle.
Recall.
c = 2x
And x = 6 cm.
c = 2*6
c = 12 cm.
Again, c is the length of the inscribed rectangle.
tanf = 6/12
f = atan(½)°
g = ½*f
g = 0.5atan(½)°
h = (12-y) cm.
tan(0.5atan(½)) = y/(12-y)
y = 0.2360679775(12-y)
1.2360679775y = 2.83281573
y = 2.83281573/1.2360679775
y = 2.2917960675 cm.
Where y is the radius of the inscribed red circle.
It implies; area green is;
Area rectangle with length 12 cm and width 6 cm - Area circle with radius 2.2917960675 cm.
(12*6)-(2.2917960675²π)
= 72-16.5
= 55.5 cm²
