Calculating green inscribed circle circumference.Let y be the radius of the green inscribed circle.Notice.ABCD is a square.Let x be the side length of the square which is also the radius of the inscr...
Calculating x (AD).a = 6-5a = 1 unit.tanb = 3/1b = 71.5650511771°Notice.b is angle theta (angle ADC = angle BAD).c = (180-b)+(90-b)c = (180-71.5650511771)+(90-71.5650511771)c = 126.869897646°c is ang...
Calculating Area Inscribed SquareLet x be the length of the ascribed rectangle.a²+2² = x²a = √(x²-4) units.Calculating x.2 ~ √(x²-4)√(x²-4) ~ 1Cross Multiply.2 = x²-4x² = 6x = √(6) units.Again, x is...
Calculating the required red length.Let x be the side length of the ascribed square.a = ½(x) units.b = ⅓(x) units.tanc = (⅓(x))/xc = atan(⅓)°d = 180-45-cd = 135-atan(⅓)d = 116.565051177°Calculating x...
Calculating length H.Let r be the radius of the circle.a = 2r units.a is the diameter of the circle.b = 4+2+3b = 9 units.c = 2+3c = 5 units.d²+r² = 5²d = √(25-r²) units.e = r+de = (r+√(25-r²)) units....
Calculating Area Blue.Let r be the radius of the biggest circle, also the side length of the blue square.a = 4+9a = 13 units.b = (r-4) units.c = (r-9) units.d = (r+9) units.e = (r-9) units.It implies...
Calculating Area Inscribed Blue Triangle (Equilateral Triangle).Let r be the radius of the inscribed six congruent circles.a+a+r+r = 52a = 5-2ra = ½(5-2r) units.b = ⅙*180(6-2)b = 120°c = ½(b)c = 60°C...
Calculating angle x.Let BE be 1 unit.a = 180-55-20a = 105°a is angle CBE.b = a-30b = 105-30b = 75°b is angle ABE.(1/sin20) = (c/sin105)c = 2.82417818114 units.c is CE.d = 180-55-15-75d = 180-145d = 3...
Calculating area blue.tana = 24/32a = atan(3/4)°b² = 24²+32²b = √(24²+32²)b = 40 units.c = b-20c = 40-10c = 30 units.40 ~ 3024 ~ dCross Multiply.40d = 30*24d = ¼(3*24)d = 18 units.d is the top parall...
Calculating blue area.tana = 0.5(10)/10a = atan(½)°.b = 90-ab = atan(2)°.c = 180-45-ac = 135-atan(½)c = 108.434948823°It implies;(10/sin108.434948823) = (d/sin45)d = 7.453559925 cm.Therefore, area bl...
