Calculating yellow area.Notice. 12 square units is the area of the red quarter circle.¼*πa² = 12πa² = 48a = √(48/π)a = 3.90882009522 units.a is the radius of the red quarter circle.b² = 2a²b = √(2*3....
Calculating length x.sina = 6/10a = asin(3/5)°b = 90-ab = (90-asin(3/5))°c²+6² = 10²c = √(100-36)c = 8 units.d =20-8d = 12 units.e = 20-6-6e = 8 units.It implies, length x is;x² = d²+e²x² = 12²+8²x²...
Calculating length MN.let x be the radius of the circle.a = ½(15)a = 7.5 units.b = 24-ab = 24-7.5b = 16.5 units.c²+b² = 24²c = √(24²-16.5²)c = 17.4284250579 units.d²+a² = x²d = √(x²-7.5²) units.e = x...
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 pink inscribed triangle.x² = 8²+6²x² = 100x = 10 units.x is the diameter of the ascribed circle.a = ½(10)a = 5 units.a is the radius of the ascribed.tanb = 8/6b = atan(4/3)°tanc = 6/...
Calculating area rectangle ABCD.Let AB = CD be x.Let AD = BC be y.Therefore;y ~ 2√(6)2√(6) ~ xCross Multiply.xy = 2√(6)*2√(6)Where xy is the area of rectangle ABCD.It implies;xy = 4*6xy = 24 square u...
Calculating the ascribed triangle.1² = 3²+3²-2*3*3cosa18cosa = 18-1a = acos(17/18)a = 19.1881364537°b = ½(180-a)b = 0.5(180-19.1881364537)b = 80.4059317732°c = 180-bc = 180-80.4059317732c = 99.594068...
Calculating OM/ON.Let x be the radius of the inscribed circle.a = (4+x) units.a is AC.b = (6+x) units.b is AB.c = 4+6c = 10c is BC.Calculating x.a²+b² = c²(4+x)²+(6+x)² = 10²16+8x+x²+36+12x+x² = 1002...
Calculating x, a chord of the inscribed green circle.Notice.a = 2 cm.b = 6 cm.d = a+bd = 2+6d = 8 cm.d is the diameter of the ascribed yellow circle.r = ½(a+b)r = ½(2+6)r = 4 cm.r is the radius of th...
Calculating GH/HI.Let 2 units be the side length of the regular pentagon.Therefore, 1 unit is the radius of the circle.a = ⅕*180(5-2)a = 108°a is the single interior angle of the regular pentagon.b =...
