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...
Calculating Area of the Red Rectangle.Let x and y be the length and width of the red rectangle respectively.tana = 4/3a = atan(4/3)°b = 90-ab = atan(3/4)°c = ½(180-a)c = ½(180-atan(4/3))°d = ½(180-b)...
Calculating (x-y).Let the base of the ascribed triangle be 1 unit.a = 180-50-20-40-30a = 40°a is (x+y).cos(40+30) = (0.5*1)/bb = 0.5/cos70b = 1.46190220008 units.c = 180-20-40c = 120°(1/sin120) = (d/...
Calculating Area BCDA, Area of the Square.Let x be the side length of the square.½*a*x = 9ax = 18a = (18/x) units.a is CP.b = x-ab = x-(18/x)b = (x²-18)/x units.Notice.c = 25-9c = 16 square units.c i...
Calculating Angle alpha and the circumference of the inscribed circle.Let alpha be x.Notice.32π cm² is the area of the ascribed half circle.Calculating R, radius of the ascribed half circle.½*πR² = 3...
Calculating R, radius and circumference of the ascribed circle.a = √(3) units.a is the side length of the blue inscribed square.b = √(5) units.b is the side length of the green inscribed square.c = √...
