Calculating R, radius and circumference of the ascribed circle.a = √(3) units.a is the side length of the blue inscribed square.b = √(5) units.b is the side length of the green inscribed square.c = √...
Calculating Area Blue.Notice.The inscribed triangle is equilateral.Area Blue is;Area sector with radius 10 cm and angle 60° - Area sector with radius 5 cm and angle 120° - Area equilateral triangle w...
Calculating Blue Area.Let x be the side length of the big inscribed blue square.a = ½(10)a = 5 units.a is the radius of the half circle.b = ½(x) units.Calculating x.5² = x²+(½*x)²25 = x²+¼(x²)25 = ¼(...
Calculating Green Area.Let x be the side length of the square.a = ½(x) units.a is the radius of the inscribed half circle.tanb = ½(x)/xb = atan(½)°c = 2bc = 2atan(½)°d = 90-cd = (90-2atan(½))°d = 36....
Calculating x, the radius of the big quarter circle.a = ½(90)a = 45°a is half angle DBE.b = ½(180-45)b = 67.5°b is angle BDF.c = (x+1) units.c is AB.d = (x-1) units.Therefore, x is;tan67.5 = (x+1)/(...
Calculating Area Pink Regular Hexagon.Let a be the side length of the pink regular hexagon.Let b be the side length of the red regular hexagon with area 6 square units.A nice analysis of the composit...
Calculating Area Triangle APC, Area Yellow.Let x be AP = CPa = ½(10)a = 5 cm.a is the mid-point of AC.Notice.Since angle BAP = angle CAP is equal and length AP = length CP.It implies;AB = 5 cm.cosb =...
Calculating the required inscribed orange triangle area.a = ½(3)a = 1.5 units.a is the radius of the inscribed circle.tanb = 3/4b = atan(3/4)°tan(atan(3/4)) = c/1.53/4 = c/1.54c = 4.5c = 1.125 units....
Calculating Area ADCB, a Cylic Quadrilateral.a = ½(45)a = 22.5°a is angle CBD.b = a+45b = 22.5+45b = 67.5°b is angle ABE.sin67.5 = 10/cc = 10.8239220029 units.c is AB = AD.d² = 2c²d² = 2*10.823922002...
Calculating Alpha.Let it be x.Let a be the radius of the ascribed quarter circle.b = (a-√(2)) units.c = (a-2√(2)) units.Calculating a.a ~ (a-√(2))(a-2√(2)) ~ √(2) Cross Multiply.√(2)a = a²-2√(2)a-√(2...
