8 = 4
a = (8-a) Cross multiply.
64-8a = 4a
64 = 12a
a = ⅓(16) cm.
b = 8-a
b = ⅓(8) cm.
c = atan(⅔)°
d = atan(3/2)°
⅔ = 8/e
e = 12 cm
⅔ = f/8
f = ⅓(16) cm.
g = 8-f
g = ⅓(8) cm.
Area Orange ex...
Let AB be 1 unit.
a = 180-24-45
a = 111°
a is angle AED.
(1/sin111) = (b/sin24)
b = 0.43567391896 units.
b is ED.
c = √(2) units.
c is BD.
d = √(2)-0.43567391896
d = 0.97853964341 units.
d is BE...
Let the square side be 2 units.
tan30 = a/2
a = 2/√(3) units.
a is BK.
b = 2-a
b = (2-(2/√(3))) units.
b is CK.
tan30 = (2-(2/√(3)))/c
c = (2√(3)-2) units.
c is CM.
d = 2-c
d = 2-(2√(3)-2)
d = (...
Let AB = CD = 2 units.
Let the big inscribed square side length be a.
Considering similar triangle ratios, calculating a.
(a-2) = (2+a)
2 = a
Cross Multiply.
a²-2a = 4+2a
a²-4a-4 = 0
(a-2)²...
Let the square side be 2 units.
a = atan(2)
b = (180-atan(2))°
(2/sin(180-atan(2))) = (1/sinc)
c = 26.56505117708°
d = 180-(180-atan(2))-26.56505117708
d = 36.86989764584°
e = 90-2d
e = 90-2*36...
Calculating green area.
a² = 5²+5²
a = √(50)
a = 5√(2) units.
b = ½(a)
b = ½(5√(2)) units.
b = 3.53553390593 units.
5² = (5-c)²+(½(5√(2)))²
25 = 25-10c+c²+¼(50)
c²-10c+¼(50) = 0
4c²-...
a² = 10²+16²-2*10*16cos120
a = 2√(129) units.
Where a is length AC.
(3√(129)/sin120) = (16/sinb)
b = 37.58908946897°
c = 90-b
c = 52.41091053103°
d = 60-b
d = 22.41091053103°
e = 90-d
e = 67.5...
Let the radius of the inscribed half circle be 1 unit.
Area rectangle is;
2*1
= 2 square units.
Calculating Shaded Area as a single fraction..
It is;
½(1*2) - 1² + ¼(1)²π - ((180-2atan(½))π*1²/...
Notice;
½(R) units is the radius of the inscribed half circle.
Therefore;
The length of the ascribed square is;
2*½(R)
= R units.
tana = (R/(0.5R)
a = atan(2)°
b = (180-2ata(2))...
Let the square side be 2 units.
Calculating the radius of the yellow circle inscribed triangle BGE.
Let it be x.
(0.5)²+1 = a²
a = ½√(5) units.
a is EG = BG.
x+2(½√(5))x = 1
(1+√(5))x = 1
x = 1/...
