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 =...
Let 1 unit be the side length of the bigger inscribed square.a = atan(½)°b = atan(2)°The required angle is;½(180-a-b)= ½(180-atan(½)-atan(2))= ½(180-90)= ½(90)= 45°
Calculating the inscribed red square area.Let x be the side length of the inscribed red square.a = 0.5+x+0.5a = (1+x) m.b = 0.5+0.5b = 1 m.It implies;a² = b²+b²(1+x)² = 1²+1²1+2x+x² = 2x²+2x-1 = 0(x+...
Calculating Area Green.Let r be the radius of the quarter circle.a = 2r units.a is the diameter when the quarter circle been a complete circle.b²+3² = 5²b² = 25-9b = √(16)b = 4 units.b is CD.c = 3+5...
Calculating Area Yellow.Notice.8 units is the side length of the regular heptagon.a = ⅐*180(7-2)a = ⅐(900)°a is the single interior angle of the regular heptagon.b² = 8²+8²-2*8*8cos(900/7)b = 14.4155...
Calculating Area BAC.Notice.The red length is the diameter of the circle.AB = 6 units.tana = 3/6a = atan(½)°b = 2ab = 2atan(½)°tan(2atan(½)) = c/6c = 6tan(2atan(½))c = 8 units.It implies, area BAC is...
