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/...
a = atan(6/12)
a = 26.56505117708°
a = Angle BAE.
b = 45-26.56505117708
b = 18.43494882292°
b = Angle CAE.
d = ½√(2*12²)
d = 6√(2) cm.
d = half AC = radius of the circle.
Let the centre of the ci...
Let the square side, x be 1 unit.
sin67.5 = a/1
a = 0.92387953251 units.
cos67.5 = b/1
b = 0.38268343237 units.
c = 2b
c = 0.76536686473 units.
d² = 1²+1²
d = √(2) units.
sin67.5...
Let the radius of the semi circle be 1 unit.
cos20 = a/2
a = 1.87938524157 units.
cos20 = 1/b
b = 1.06417777248 units.
c = a-b
c = 0.81520746909 unit.
Where c is AB, the side of the square.
Ar...
Let the square side be 2 units.
Notice;
a+b = c --- (1).
2√(2) = c+a
2√(2)-a = c --- (2).
a² = 2d²
d = (a/√(2)) units.
e = 2-d
e = (2-(a/√(2))) units.
b² = (2-(a/√(2)))²+(a/√(2))²
b² = 4-(4a/√(...
Let the side of the regular pentagon be 1 unit.
Calculating Area Red.
a² = 1²+1²-2*1*1cos108
a = 1.61803398875 units.
b = 108-36-60
b = 12°
(c/sin12) = (1.61803398875/sin96)
c = 0.33826121272 un...
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a² = 15²+12²-2*12*15cos120
a = 23.43074902772 cm.
Where a is the side length of the equilateral triangle ABC.
(23.43074902772/sin120) = (12/sinb)
b = 26.32950349168°
c = 60-b
c = 33.67049650832°...
