Calculating x, chord of the circle..a² = 1 square units.a = 1 unit.a is the side length of the 3 inscribed equal squares.b = 1+½(1)+yb = (1.5+y) units.c = 1+1c = 2 units.d² = 2²+0.5²d² = 4+0.25d = √(...
Blue area is;Area sector with radius 12 units and angle 30° - Area sector with radius 6 units and angle 60° - Area triangle with height 6 units and base 6sin120 units.= (30π*12²/360) - (60π*6²/360) -...
Calculating Length CF.a² = 4²+4²-2*4*4cos150a = 7.72740661031 cm.Where a is BE.b = angle ABE = ½(180-150)b = 15°c = angle AFE = 180-45-15c = 120°(4/sin120) = (d/sin45)d = 3.26598632371 cm.Where d is...
Calculating Length FG.tan15 = a/4a = 1.07179676972 cm.Where a is AD.b² = 1.07179676972²+4²b = 4.14110472164 cm.Where b is DF.c = 4-1.07179676972c = 2.92820323028 cm.Where c is CD.sin60 = d/2.92820323...
Calculating Shaded Area ( Triangle AEF).a = asin(1/6)b = 2ab = 2(asin(1/6))Where b is angle BAC.sin(2(asin(1/6))) = c/6c = ⅓(√(35)) units.c = 1.97202659437 units.Where c is BE.d = 90-2asin(1/6)d = 70...
Calculating Area Shaded.tan60 = a/5a = 5√(3) cm.Where a is AD.b = ½(a)b = ½(5√(3)) cm c = atan((½(5√(3))/5)c = atan(½√(3))Where c is angle AGBd = atan(5√(3)/5)d = atan(√(3))Where d is angle CAG.e = 1...
Calculating Area Shaded STR (Triangle).Let the square side be a.tan60 = a/bb = a/tan60 cm.Where b is BS.Calculating a.2b+a = 62(a/tan60)+a = 6a((2/tan60)+1) = 6a = 6/((2/tan60)+1)a = 6(2√(3)-3) cm.Ar...
Calculating Area Green Region.a² = 10²+10²-2*10*10cos150a = 19.31851652578 cm.Where a is AF which is equal AE.(19.31851652578/sin150) = (10/sinb)b = 15°Where b is angle BAF.tan15 = c/10c = 2.67949192...
Calculating Length PQ.a = atan(2)°b = 180-2ab = (180-2atan(2))°Where b is angle FBP.Notice;CQ = 5 cm.Calculating FP using sine rule.Let FP be c.(c/sin(180-2atan(2))) = (5/sin(atan(2)))c = 4.472135955...
Let the small inscribed square side be a.Let b be the side of the big inscribed square.It implies;b = 10-aTherefore;Calculating a.tan(90-75) = a/(10-a)a(1+tan15) = 10tan15a = (10tan15)/(1+tan15)a = ⅓...
