Calculating The Required Shaded Area.
Let it be x.
a² = 1²+0.5²
a = √(1.25) units.
b = 2a
b = 2√(1.25) units.
tanc = 1/0.5
c = atan(2)°
tan(atan(2)) = d/√(1.25)
2 = d/√(1.25)
d...
Calculating Length x.
a² = 2²+(2+1)²
a = √(13) units.
a is the each of the two adjacent lengths of the green isosceles right-angled triangle.
tanb = 3/2
b = atan(3/2)°
c = 45-atan(2/3)...
Calculating red area.
tana = 10/5
a = atan(2)°
b = 2a
b = 2atan(2)°
c = 180-b
c = 180-2atan(2)
c = 2atan(½)°
Area red is;
Area sector with radius 5 units and angle 2atan(2)°-Area...
Calculating Area Ascribed Regular Hexagon.
Let x be the side length of the ascribed regular hexagon.
a² = 2x²-2x²cos120
a = √(3)x units.
a is DF.
sin60 = b/x
b = ½√(3)x units.
sin30...
Calculating Angle FGM (angle alpha).
Let the single side length of the hexagon be 2 units.
Therefore;
AG =√(8-8cos150) units.
Calculating AH.
AH = √((8-8cos150)+4-4√(8-8cos150)cos105)...
Sir Mike Ambrose is the author of the question.
Calculating Area Blue ÷ Area ABCD Exactly.
Let the single side length of the inscribed regular hexagon be 2 units.
Therefore;
Area rectangle...
Calculating Area red inscribed semi circle ÷ Area green rectangle.
Let the radius of the inscribed red semi circle be r.
Therefore;
(8-r)²+(9-r)²=r²
64-16r+r²+81-18r+r²=r²
r²-34r+145...
Calculating area of the ascribed square.
a = (2+r) cm.
r is the radius of the circle yellow quarter circle.
a is AB, the side length of the ascribed square.
2(2+r)² = b²
b² = 2(4+4r+r²)
b...
Calculating Area Blue.
Let x be the side length of the ascribed square, equal a side length of the inscribed regular triangle.
Calculating x.
½*x*xsin60 = 16
¼√(3)x² = 16
√(3)x² = 64
x...
Calculating Area Red Inscribed Half Circle.
Let x be the radius of the inscribed half circle.
Calculating x.
2(6*x) = 6*6sin60
12x = 36sin60
x = 3*½√(3)
x = ½(3√(3)) units.
Again, x is...
