Calculating Area Green ÷ Area Red.Let 2 units be the length of the ascribed rectangle.Let x be the radius of the green inscribed circle.Let y be the radius of the red inscribed half circle.Notice.a =...
Calculating x (AD) the diameter of the half circle.a² = 2²+11²+2*2*11cosya² = 125+44cosy --- (1).a² = x²+7²-2*7*xcosya² = x²+49-14xcosy --- (2).Where a is AC.cosy = 7/x --- (3).Equating (1) and (2).1...
Calculating x, angle CED.Notice.AB = DE, and BC = CD.Let BC = CD = 1 unit.a = 180-100a =. 80°a is angle ACB.b = 180-65-ab = 180-145b = 35°b is angle BAC.(c/sin80) = (1/sin35)c = 1.71695992129 units.c...
Calculating length AB.a² = 6²+4²-2*4*6cos60a² = 52-24a = √(28) units.a = 2√(7) units.a is BD.(√(28)/sin60) = (4/sinb)b = 40.8933946491°b is angle CBD.c = 60-bc = 19.1066053509°c is angle ABD.d = 180-...
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...
