Calculating Area Yellow.a = ½(180-30)a = 75°2² = b²+1²b² = 4-1b = √(3) units.Yellow Area is;2(Area triangle with height √(3) units and base 1 unit + Area sector with radius 2 units and angle 60° - Ar...
Calculating length AD.Let AD be x.Let alpha be y.Notice.AB = CD = 6 cm.a = (x+6) cm.tany = x/6 --- (1).tan(2y) = 6/(x+6) (2tany)/(1-tan²y) = 6/(x+6) --- (3).Calculating x.Substituting (1) in (3).(2ta...
Calculating (length Blue + length red)/(length yellow).Let r be the radius of the circle.Calculating r.πr² = 144πr² = 144r = 12 cm.a = 2ra = 24 cm.a is the diameter of the circle.Let b be the blue le...
Calculating length FB.Notice.Triangle BCF is equilateral.It Implies;Let FB = CB = FC = x.(17/sin60) = (15/sina)sina = (15sin60)/17a = 49.8305486955°a is angle BFD.b = 180-60-ab = 70.1694513045°Theref...
Calculating Blue Area.a = ½(2)a = 1 unit.a is the radius of the inscribed half circle.tanb = 2/1b = atan(2)°c = 2bc = 2atan(2)°d = 180-cd = 2atan(0.5)°Blue Area is;Area sector with with radius 1 unit...
Sir Mike Ambrose is the author of the question.Let the side length of the square be 2 units.Therefore area ABD (equilateral triangle) is;Area triangle with height 2 unit and base (2sin60) units.= ½*2...
Sir Mike Ambrose is the author of the question.Let the single side length of the square be 2 units.Therefore;Area Square is;2²= 4 square units.Area Green is;Area triangle with height √(3) units and b...
Calculating r, radius of the circle.a = 5+6a = 11 units.b = ½(a) b = 5.5 units.c = 180-60c = 120°It implies;d² = 3²+6²-2*3*6cos60d² = 45-18d = √(27)d = 3√(3) units.((3√(3))/sin60) = (6/sine)e = 90°f²...
Calculating d, the diameter of the circle.Let r be the radius of the circle.a*4 = 2*22a = 11 units.b = 22+2b = 24 units.c = ½(b)c = 12 units.d = ½(11+4)-4d = 7.5-4d = 3.5 units.Radius r of the circle...
Calculating x.Let AD = y.x² = y²+32²-2*32*ycosax² = y²+1024-64ycosa --- (1).x² = y²+17²-2*17*ycosax² = y²+289+34ycosa --- (2).Calculating y.Equating (1) and (2).y²+1024-64ycosa = y²+289+34ycosa1024-6...
