Calculating yellow area.
Notice.
Area of the ascribed square is 12 square units.
Area yellow is;
½(12) - (½(⅔√(3))²sin(atan(3))÷sin(135-atan(3)))sin(45)
= 6 - (½)
= ½(12-1)
= ½(11)...
Calculating Area Red.
Area red is;
½(3*4) - (atan(4/3)*9π÷ 360) - (atan(3/4)*4π÷ 360)
= 0.54016930141 square units.
Calculating Area Rectangle.
Let r be the radius of the half circle and also, the width of the rectangle.
a = r+r
a = 2r units.
a is the diameter of the half circle.
b = (2r-x) units.
b...
Sir Mike Ambrose is the author of the question.
Let the single side length of the regular hexagon be 2 units.
Area rectangle is;
2.5x√(3)
= ½(5√(3)) square units.
Area green is;
Are...
Calculating Area Green.
Let x be the side length of the ascribed square.
a = ½(x) units.
tanb = x/(½(x))
b = atan(2)°
c = 180-45-atan(2)
c = (45+atan(½))°
It implies;
(0.5x/sin(...
Calculating Angle x.
Let AC = 1 units.
sin(10+10) = a/1
a = 0.34202014333 units.
a is BC.
tan40 = b/0.34202014333
b = 0.28698897612 units.
c = 180-10-30-40
c = 100°
(1/sin100) =...
Calculating Yellow Area.
2a² = 2²
a = √(2) units.
a is the radius of each of the two congruent half circles.
2b² = (2+1)²
b² = ½(9)
b = ½(3√(2)) units.
b is the radius of the circle....
Calculating angle x.
a = 180-2(48)
a = 180-96
a = 84°
b = 180-72-a
b = 180-72-84
b = 180-156
b = 24°
c = ½(180-72)
c = ½(108)
c = 54°
d = 90-c
d = 90-54
d = 36°
Therefore, t...
Calculating Area Blue.
a = 5+3
a = 8 units.
a is the side length of the big square.
b² = 3²+8²
b² = 9+64
b = √(73) units.
c = ½(b)
c = ½√(73) units.
c is the side length of the two e...
Calculating Shaded Area Blue.
a² = 4²+3²
a = √(25)
a = 5 units.
a is the radius of the quarter circle.
5 ~ 4
3 ~ b
Cross Multiply.
5b = 12
b = 2.4 units.
d² = 5²+3²
d = √(34) units...
