Calculating Angle Theta.Let theta be a, angle CAD.b = 180-40-80b = 60°b is angle BCD.Let X = 1 unit.X is BD.(1/sin60) = (Y/sin80)Y = 1.1371580426 units.Y is BC.(c/sin40) = (1/sin60)c = 0.74222719897...
Calculating the required red angle.Let it be x.Notice.The composite plane shape is not drawn to scale.Let the both equal lengths that makes the hypotenuse of the ascribed right-angled triangle be 1 u...
Calculating length BA, diameter of the small half circle.a = 3+12+5a = 20 units.a is the diameter of the big half circle.b = ½(a)b = ½(20)b = 10 units.b is the radius of the big half circle.Let x be...
Calculating ratio area yellow square to area red square.Let the side length of the inscribed yellow square be 2 units.It implies yellow square area is;2²= 4 square units.a = (2+x) units.Where x is th...
Calculating area A (Area of one of the two inscribed equal squares).Let their side length be x each.a = 4+9a = 13 units.b = x+xb = 2x units.c²+4² = (2x)²c = √(4x²-16) units.d = 2cd = 2√(4x²-16) units...
Calculating Area Triangle CBA.Let the two equal lengths of the ascribed isosceles right-angled triangle be x.It implies;4² = 2²+x²-2*2xcosa16 = 4+x²-4xcosa12 = x²-4xcosa --- (1).b = (90-a)°(2√(2))² =...
Calculating Area Green.a = 12+8a = 20 units.a is BG.tanb = 12/20b = atan(3/5)°b is angle DAH.c = 180-45-bc = (135-atan(3/5))°(12/sin(135-atan(3/5))) = (d/sin(atan(3/5)))d = 6.36396103068 units.d is D...
Calculating yellow shaded area (equilateral triangle).Let x be CE.a = 4-3a = 1 unit.b²+3² = x²b = √(x²-9) units.b is AE.c²+4² = x²c = √(x²-16) units.c is BE.d = b+cd = (√(x²-9)+√(x²-16)) units.d is A...
Calculating yellow area.Let x be each of the three congruent red lengths.Let y be each of the two congruent blue lengths.a = (x+3) units.It implies;√(129)² = (x+3)²+x²+2x(x+3)cosb129 = 2x²+6x+9+(2x²+...
Calculating Area Blue.Let x be the base of the inscribed white right-angled triangle with hypotenuse 10 units.a² = 10²+10²a = √(2(10²))a = 10√(2) units.a is the hypotenuse of the ascribed right-angle...
