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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3626194

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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 = 135°b is the single interior angle of the regular octagon.c² = 4²+4²-2*4*4cos120c² = 32+16c² = 48c =4√(3) units.tand = 2/(4√(3))d = atan(1/(2√(3))d = 16.102113752°e = 120-30-de =120-30-16.102113752e = 73.897886248°f = 180-ef = 180-73.897886248f = 106.102113752°g = 360-a-bg = 360-120-135g = 105°h = g...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3626115

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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 = (y+1) units.b is length AC.y is the side length of square ABFG.Calculating y.√(2)² = y²+(y+1)²2 = y²+y²+2y+12y²+2y-1 = 0y²+y = ½(y+½)² = ½+(½)²(y+½)² = ¾y = -½±√(¾)y = -½±½√(3)It implies;y ≠ -½(1+√(3)) units.y = ½(√(3)-1) units.y = 0.36602540378 units.Again, y is the side length of square ABFG.Re...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3625773

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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°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3624354

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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+1)² = 1+1²x+1 = ±√(2)x = -1±√(2)Therefore;x ≠ -1-√(2)x = (√(2)-1) m.Again, x is the side length of the inscribed red square.It implies x², area red inscribed square is;(√(2)-1)²= 2-2√(2)+1= (3-2√(2)) m²= 0.17157287525 m²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3623064

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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 units.c = 8 units.c is length DE plus Length CE.(2r)² = 8²+4²4r² = 64+164r² = 80r² = 20r = 2√(5) units.Again, r is the radius of the quarter circle.d²+r² = 5²d² = 5²-(2√(5))²d² = 25-20d = √(5) units.d is BE.It implies, green area is;½*r*d½*2√(5)*√(5)= 5 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3622037

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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 = 14.4155018864 units.c = ½(180-(900/7))c = 25.714285°d = (900/7)-cd = (900/7)-25.714285d = 102.857143571°e² = 14.4155018864²+4²-2*14.4155018864*4cos102.857143571e = 15.7945782971 units.(15.7945782971/sin102.857143571) = (4/sinf)f = 14.2942589329°g = c+fg = 25.714285+14.2942589329g = 40.0085439329°h = 180-d-...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3622035

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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;½*6*8= 24 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3621356

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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)d = ½(180-atan(3/4))°tan(½(180-atan(4/3))) = 3/ee = 3/tan(½(180-atan(4/3)))e = ½(3)e = (3/2) units.tan(½(180-atan(3/4))) = 4/ff = 4/tan(½(180-atan(3/4)))f = ⅓(4)f = (4/3) units.Therefore;x = 4+(4/3)x = ⅓(16) units.Again, x is the length of the red rectangle.y = 3+(3/2)y = ½(9) units.Again, y is the...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3620930

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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/sin20)d = 0.39493084363 units.e² = 0.39493084363²+1.46190220008²-2*0.39493084363*1.46190220008cos30e = 1.13715804261 units.Calculating y.(1.13715804261/sin30) = (0.39493084363/siny)y = asin(0.39493084363sin30/1.13715804261)y = 10°It implies, (x-y) is;Recall.x+y = 40And y = 10°x = 40-10x = 30°Therefo...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3620926

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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 is area BPQ.And triangle ABQ is equal triangle DPQ.It implies;Area BCDA, x² is;x² ~ 25((x²-18)/x)² ~ 16x ~ 5(x²-18)/x ~ 4Cross Multiply.4x = 5(x²-18)/xCross Multiply Again.4x² = 5(x²-18)4x² = 5x²-905x²-4x² = 90x² = 90 square units.Again, x² is area BCDA, area of the square.
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