Sir Mike Ambrose is the author of the question.
Area Red is;
Area triangle with height 2 units and base 2sin(180-2ata(¾)) units.
= ½*2*2sin(180-2ata(¾))
= 2sin(180-2ata(¾))
= 48/25 squar...
Calculating Shaded Black Area.
a² = 9²+12²
a = √(81+144)
a = 15 units.
a is the hypotenuse of the ascribed right-angled triangle.
b = ½(a)
b = 7.5 units.
tanc = 9/12
c = atan(3/4)°...
a = ⅑*180(9-2)
a = 140°
a is the single interior angle of the regular nonagon.
b = ½(180-140)
b = 20°
c = 140-20
c = 120°
d = ½((180(5-2))-3*140)
d = ½(540-420)
d = ½(120)
d = 60°...
6² = a²+(2+3)²
a² = 36-25
a = √(11) units.
b² = 3²+c²
b = √(9+c²) units.
b is the diameter of the circle.
d = c-a
d = (c-√(11)) units.
e² = 2²+(c-√(11))²
e = √(4+c²-2c√(11)+11)
e =...
a = 0.5*5*5sin40
a = 8.0348451211 square units.
(b/sin40) = (5/sin70)
b = 3.4202014333 units.
c = 0.5*3.4202014333*3.4202014333sin40
c = 3.7595933295 square units.
Shaded Area is:
a...
sin60 = 0.5d/a
a = ⅓√(3)d units.
a is the radius of the half circle.
Therefore, total blue area in terms of d is;
2(60π*⅓√(3)d*⅓√(3)d/360)+(0.5*⅓√(3)d*⅓√(3)dsin120)-(0.5*⅓√(3)d*⅓√(3)dsin60)...
a = ½(d) units.
a is the radius of the green half circle.
b = d+a
b = ½(3d) units.
c² = (½(3d))²-(½(d))²
c² = ¼(8d²)
c = √(2(d)²)
c = √(2)d units.
c is the diameter of the small blue se...
Notice!
Triangle ABM is equilateral.
Calculating a:b.
Let AB be 1 unit.
c = 90-60
c = 30°
cos30 = (0.5*1)/d
d = ½÷½√(3)
d = 1/√(3)
d = ⅓√(3) units.
d is the radius of the semi cir...
a = ⅓(90)
a = 30°
sin30 = b/4
b = 2 cm.
sin60 = c/4
c = 2√(3) cm.
d = √(4²-2²)-√(4²-(2√(3))²)
d = √(12)-√(4)
d = (2√(3)-2) cm.
d = 1.4641016151 units.
Area Blue is;
Area trapez...
