Calculating Shaded Area.
Notice.
The ascribed square side length is 1 unit.
tana = 1/½
a = atan(2)°
b = 2a
b = 2atan(2)°
c = b-90
c = 2atan(2)-90
c = 36.8698976458°
d = 180-b
d = 180-2atan(2)...
Calculating Blue Shaded Area.
Let a be the radius of each of the circle with area 10 square units.
Calculating a.
πa² = 10
a² = 10/π
a = √(10/π) units.
a = 1.78412411615 units.
Area...
Calculating r, radius of the inscribed semicircle.
15² = 13²+14²-2*13*14cosa
2*13*14cosa = 13²+14²-15²
cosa = (13²+14²-15²)/(2*13*13)
a = 67.380135052°
It implies, r is;
13r+14r = 13*14sin67.3801...
Calculating Area Square.
Let x be the side length of the square.
a²+x² = 3²
a = √(9-x²) units.
b = x-a
b = (x-√(9-x²)) units.
Therefore;
x/3 = (x-√(9-x²))/2
Cross Multiply.
2x =...
Calculating Area Blue.
Let a be the side length of the ascribed quarter circle.
tan30 = 2/b
b = 2√(3) units.
c = (a-2) units.
d = (2√(3)+½(a))
d = ½(4√(3)+a) units.
Calculating a.
(a-2)² = (½(...
Calculating Area Yellow, Area of The Inscribed Half Circle.
4r+3r = 4*3
7r = 12
r = ⅐(12) units.
r is the radius of the inscribed yellow half circle.
Area Yellow Inscribed Half Circle is;...
Calculating Area Green.
sin30 = a/12
a = 6 units.
b²+6² = 12².
b = √(144-36)
b √(108)
b = 6√(3) units.
sin60 = c/12
c = 6√(3) units.
d² = 12²-(6√(3))²
d = √(144-108)
d = √(36)
d = 6 units.
The...
Calculating Shaded Green Area.
sin30 = a/2
a = 1 unit.
(a')²+1² = 2²
a' = √(4-1)
a' = √(3) units.
a'' = 2a'
a'' = 2√(3) units.
a'' is the side length of the inscribed regular triangle.
b² = 2²+2...
Calculating Length x.
x ~ ½(2)
(2+7) ~ x
Cross Multiply.
x² = 9
x = √(9)
x = 3 units.
Calculating Area Blue Triangle.
a² = 2(2)²
a = 2√(2) units.
a is the diagonal of a square.
b = ½(180-30)
b = 75°
c = b-45
c = 75-45
c = 30°
sin30 = d/a
½ = d/(2√(2))
d = √(2) units.
d is the bas...
