Calculating Area Blue.Let x be the side length of the inscribed regular pentagon.a = ⅕*180(5-2)a = 108°a is the single interior angle of the inscribed regular pentagon.b² = 2x²-2x²cos108b = 1.6180339...
Calculating Area Green.Notice.The composite plane shape is drawn to scale.a = 6 cm.Let b = x cm.b is the width of the inscribed rectangle.c = 2x cm.c is the length of the inscribed rectangle.d² = x²+...
Calculating Area Green Square.Let x be the side length of the green square.a = (100-x) m.a is the side length of the orange square.Calculating x.x²+(100-x)² = 5018x²+10000-200x+x² = 50182x²-200x+1000...
Calculating pink area.Notice.The triangle is equilateral.a = 90-60a = 30°tan30 = b/2b = ⅓(2√(3)) m.It implies;Area pink is;Area square with side 2 m - Area triangle with height 2 m and base ⅓(2√(3))...
Calculating x, length OP.a² = 2²+6²a = √(40) units.a is BC.tanb = 6/2b = atan(3)°b is angle PBC.cosc = (0.5√(40))/√(50)c = acos(√(10)/√(50))c is angle PBC.d = b-cd = atan(3)-acos(√(10)/√(50))d = 8.13...
Calculating Area Green Circle.Let x be the radius of the circle.x is the height of the pink area.a = x+⅓(x)a = ⅓(4x) cm.a is the base of the pink area.Calculating x².½*x*⅓(4x) = 27⅓(2x²) = 272x² = 81...
Calculating Area Pink Square.a = √(2) m.a is the side length of the green square.b = √(1)b = 1 m.b is the side length of the purple square.Let x be the side length of the pink square.c²+√(2)² = x²c²...
Calculating R, radius of the circle.a = ½(24)a = 12 units.b²+12² = R²b² = R²-144b = √(R²-144) units.c = 24 units.d = R+bd = (R+√(R²-144)) units.Notice.c = dTherefore R, radius of the circle is;R+√(R²...
Calculating Area Blue.Notice.The side lengths of the regular octagon and regular hexagon is 4 units each.a = ⅙*180(6-2)a = 120°a is the single interior angle of the regular hexagon.b = ⅛*180(8-2)b =...
Calculating Alpha.Let it be x.Notice.BCDE and ABFG are both square.Let the two equal red lengths be √(2) units each.a²+a² = √(2)²2a² = 2a² = 1a = 1 unit.a is the side length of square BCDE.b = y+ab =...
