Calculating Area Inscribed yellow Circle.
Let x be the area of the ascribed circle.
a*12 = 5*9
a = (45/12)
a = ¼(15) units.
a = 3.75 units.
b = ½(a+12)
b = ½(15.75)
b = 7.875 units....
Calculating Area Blue.
a = ½(4)
a = 2 units.
a is the radius of the inscribed half circle.
b = (2+x) units.
x is the radius of the inscribed circle.
c = (4-x) units.
It implies;
d²+x² = (4-x)²...
Calculating R, radius of the circle.
R² = 8²+5²-2*8*5cosx
R² = 89-80cosx --- (1).
a = (90-x)°
R² = 5²+12²-2*5*12cos(90-x)
R² = 169-120cos(90-x)
R² = 169-120(cos90cosx-sin90sinx)
R² = 1...
Calculating angle x.
Let CD = 1 unit.
(1/sin30) = (a/sin(180-20-20-30))
a = 1.87938524157 units.
a is BC.
cos20 = (½(BC))/b
cos20 = (0.5*1.87938524157)/b
b = 0.93969262079/cos20
b = 1 unit.
b is...
Calculating Area Ascribed Square.
Let x be the radius of the red inscribed circle.
a = (x-4) cm.
b = (x-6) cm.
It implies;
Calculating x.
(x-4)*(x-4) = x*(x-6)
(x-4)² = x(x-6)...
Calculating Green Area.
tana = 6/3
a = atan(2)°
b = 180-a
b = (180-atan(2))°
(6/sin(180-atan(2)) = (3/sinc)
c = 26.5650511771°
d = 180-sin(180-atan(2))-c
d = 36.8698976458°
e = 2d
e = 73.739795...
Calculating Area Triangle ABC and Length AN ÷ Length NC.
Let AB equal x.
a = (3*x)/(3+4)
a = ⅐(3x) units.
a is AT = AN.
b = (4*x)/(3+4)
b = ⅐(4x) units.
b is TB = MB.
c = a+4
c = ⅐(3x)+4
c = ⅐(3...
Calculating Blue Area.
Blue Area is;
2(area circle of radius 1 unit - 2(2(area sector of radius 1 unit and angle 60°) - area equilateral triangle of two side length 1 unit and angle 60°))
=...
Sir Mike Ambrose is the author of the question.
Calculating Area Green ÷ Area Rectangle.
Area rectangle is;
9x8 = 72 square units.
Area green is;
Area trapezoid with two parallel lengths (5+2-¾)...
Calculating Blue Area.
Let x be the radius of the ascribed half circle.
a²+7² = (2x)²
a = √(4x²-49) units.
b = a-4
b = (√(4x²-49)-4) units.
It implies;
Calculating x.
√(4x²-49) ~ x
2x ~ (√(4x²...
