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...
Calculating r, radius of the inscribed circle.Notice.Angle ABD = ¼(60)Angle ABD = 15°tan30 = r/a1/√(3) = r/aa = √(3)r units.b = 2ab = 2√(3)r units.b is the side length of the ascribed regular triangl...
Calculating the green area x.Notice.5 units is the height of the green triangle and 15 units is the base.It implies, area green (x) is;½*5*15= ½(75)= 37.5 square units.
Calculating theta.Let it be x.Let angle BAD be a.b+a+30 = 180b = (150-a)°b is angle ADB.It implies;x+b = 180x+150-a = 180x = (30+a)°Again, a is theta.c = 180-100c = 80°c is the supplementary angle of...
Calculating Angle x.a = 90-40a = 50°a is angle EOQ.b = ½(180-a)b = ½(180-50)b = ½(130)b = 65°Therefore the required angle, x is;x = ½(90)+bx = 45+65x = 110°
