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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3468427

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Calculating Area of the yellow Hexagon.Let x be the side length of the hexagon.a²+3² = x²a = √(x²-9) cm.b² = 2x²-2x²cos120b = √(3x²)b = √(3)x cm.It implies;Calculating x.sinc = √(x²-9)/x --- (1).sinc = 5/(√(3)x) --- (2).Equating (1) and (2).√(x²-9)/x = 5/(√(3)x)Cross Multiply.5x = √(3)x*√(x²-9)5 = √(3x²-27)25 = 3x²-273x² = 52x² = 52/3x = √(52/3)x = 4.16333199893 cm.Again, x is the side length of the yellow hexagon.Recall.b = √(3)x cm.And x = √(52/3) cm.b = √(3)*√(52/3)b = √(52) cm It implies;Ar...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3468425

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Calculating Area Red.a² = 6²+8²a = √(100)a = 10 cm.a is the side length of the square.6b+8b+10b = 8*624b = 48b = 2 cm.b is the radius of the inscribed circle.tanc = 6/8c = atan(3/4)°cosc = 2/dd = 2/cos(atan(3/4))d = 2.5 cm.e = 90-ce = atan(4/3)°tane = f/2.5(4/3) = f/2.5f = 2.5(4/3)f = ⅓(10) cm.f = 3.333 cm.g = (½(c)+90)°g = (0.5atan(3/4)+90)°h² = (8-2)²+2²h² = 40h = 2√(10) cm.j² = 10²+(2√(10))²-2*10*2√(10)cos(0.5atan(3/4)+90)j = 13.416407865 cm.(13.416407865/sin(0.5atan(3/4)+90)) = (2√(10)/sink...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3468422

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Sir Mike Ambrose is the author of the question.Let the side length of the square be 1 unit.Therefore;Area square is;1² = 1 square units.It implies;Area R is;Area square - Area equilateral triangle with side 1 unit - 2(area sector with radius 1 unit and angle 30°)= 1 - ½(sin60) - 2(30π÷360)= 1 - ¼(√(3)) - (π/6)= (12-3√(3)-2π)/12 square units.Therefore;Area R ÷ Area Square as a single fraction in terms of π is; (12-3√(3)-2π)/12 ÷ 1= (12-3√(3)-2π)/12

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3463370

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Sir Mike Ambrose is the author of the question.Let the side length of the be 2 units.Therefore;BC = 2 units.It implies;Area orange is;½(1*2) = 1 square units.Area green is;½(1*2) + ½(2/√(5))(4/√(5))= 1 + (4/5)= (9/5)Therefore;Area orange : Area green is;1 : (9/5)=(5*1) : (5*(9/5))= 5 : 9Proved.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3462579

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Calculating Area Red.a = (2x+6) cm.a is the height of the ascribed right-angled triangle.b = (9x+6) cm.b is the base of the ascribed right-angled triangle.c = 13x cm.c is the hypotenuse of the ascribed right-angled triangle.Calculating x.c² = a²+b²(13x)² = (2x+6)²+(9x+6)²169x² = 4x²+24x+36+81x²+108x+3684x² = 132x+7221x²-33x-18 = 07x²-11x-6 = 07x²-14x+3x-6 = 07x(x-2)+3(x-2) = 0(7x+3)(x-2) = 0It Implies;x ≠ -3/7x = 2 cm.Recall.a = (2x+6) cm.And x = 2 cm.a = 2*2+6a = 10 cm.b = (9x+6) cm.And x = 2...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3461408

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Sir Mike Ambrose is the author of the question.Calculating Area of the Triangle.Let alpha be x.Therefore;(12/sin2x)=(8/sinx)And;Sin2x = 2sinxcosxTherefore;(12/2sinxcos)=(8/sinx)6 = 8cosxx = acos(6/8)°2x = 2acos(6/8)°Let y be the third interior angle.y = (180-3acos(6/8))°It implies;Area of the triangle in cm² is;Area triangle with height 12 cm and base 8sin(180-3acos(6/8)) cm.= ½*12*8sin(180-3acos(6/8))= 48sin(180-3acos(6/8)) cm²= 39.686269666 cm².

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3460521

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Sir Mike Ambrose is the author of the question.Calculating Area Green.Area green exactly in cm² is;Area ABCD - Area trapezoid with parallel sides (9-2√(3)) cm and (24√(3)-39) cm, and height 6 cm.= (54-6√(3)) - ½*6((9-2√(3))+(24√(3)-39))= (54-6√(3)) - 3(22√(3)-30)= 54-6√(3)-66√(3)+90= 144-72√(3)= 72(2-√(3)) cm²OrCalculating Area Green.Let a be BC.tan30 = 12/bb = 12√(3) cm.b is the height of the ascribed right-angled triangle.tan30 = a/cc = √(3)a cm.d = 6+cd = (6+√(3)a) cm.tan30 = e/(6+√(3)a)e =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3459752

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Calculating Area Green Total.Area green is;Area triangle with height 8 units and base 8√(3) units - Area sector with radius 8 units and angle 30° + Area sector with radius 8 units and angle 60° - 2(area triangle with height 8 units and base 8sin60 units).= ½(8*8√(3)) - (30π*64/360) + (60π*64/360) - 2(½*8*8sin60)= 32√(3)-⅓(16π)+⅓(32π)-32√(3)= ⅓(16π) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3458768

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Sir Mike Ambrose is the author of the question.Area blue total, exactly in cm² decimal is;Area trapezoid with parallel sides (80/7) cm and ((80/7)+21.4285714284) cm, and height 20 cm - Area trapezoid with parallel sides 20 cm and ((80/7)+12.2448979591) cm, and height (60/7) cm - Area triangle with height (80/7) cm and base 12.2448979591 cm.= (½*20((80/7)+((80/7)+21.4285714284))) - (½*(60/7)(20+((80/7)+12.2448979591))) - (½*(80/7)*12.2448979591)= 442.857142855 - 187.172011662 - 69.9708454806= 18...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3457816

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Sir Mike Ambrose is the author of the question.Side length of the square is;Let it be x.x = √((16*34)-144)x = √(400)x = 20 cm.Therefore;Area Orange exactly in decimal cm² is;Half area square with side 20 cm - Area triangle with height 7.88405797101 cm and base ⅓(32sin(2atan(3/5))) cm - Area triangle with height 8.74642784227 cm and base (12sin(atan(5/3))) cm= ½(20²) - ½(7.88405797101*⅓(32sin(2atan(3/5)))) - ½(8.74642784227*(12sin(atan(5/3))))= 200 - 37.1014492753 - 45= 155 - 37.1014492753= 117....
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