Calculating a/b.Let r be the equal radius of the inscribed circle and half circle.It implies;r = ½(a) units.c = (a+b) units.c is the radius of the ascribed quarter circle.Let c be 1 unit.d = (1-½(a))...
Calculating Area Blue.Notice.The composite plane shape is not drawn to scale.a² = (3+3)²+(2+2)²-2*6*4cos120a² = 36+16+24a = √(76) units.a = 2√(19) units.a is AC.(2√(19)/sin120) = (6/sinb)b = 36.58677...
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 Blue.a = ⅛*180(8-2)a = 45*3a = 135°a is the single interior angle of the ascribed regular octagon.b = ⅙*180(6-2)b = 30*4b = 120°b is the single interior angle of the inscribed regula...
Calculating Area Green.Let x be the side length of the ascribed square.a²+3² = x²a = √(x²-9) units.b = (90-y)°siny = 3/x --- (1).7² = x²+√(x²-9)²-2x√(x²-9)cos(90-y)49 = 2x²-9-2x√(x²-9)siny58 = 2x²-2x...
Calculating C, circumference of the circle in terms of π.Let r be the radius of the circle.a = (r-6) units.b = (r+6) units.Calculating r.(r-6)(r+6) = 3*7r²-36 = 21r² = 57r = √(57) units.Therefore, ci...
Calculating x and y.a = 6+6a = 12 units.a is the diameter of the half circle.sinb = a/13b = asin(12/13)°c²+12² = 13²c² = 169-144c = √(25)c = 5 units.Calculating x.tan(0.5b) = 6/xx = 6/tan(0.5asin(12/...
Calculating length EC.Let it be x.Let y be the radius of the blue inscribed circle.It implies;a = y+y+y+ya = 4y units.a is the diameter of the ascribed circle.b²+(25+4)² = (4y)²b² = 16y²-29²b = √(16y...
Calculating x, length AD.Notice.Plane shape ABC is not drawn to scale.a = 30+30a = 60°b² = 3²+6²-2*3*6cos60b² = 45-18b = √(27)b = 3√(3) units.b is BC.(3√(3)/sin60) = (3/sinc)3sin60 = 3√(3)sincc = asi...
Calculating area red.Let x be the side length of the small square.a = ½(x) cm.b = x+ab = x+½(x)b = ½(3x) cm.It implies;½(x) ~ c½(3x) ~ xTherefore;1 ~ c3 ~ xCross Multiply.3c = xc = ⅓(x) cm.d = c+2√(1...
