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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3534488

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Calculating Radius of the inscribed blue circle.Let R be radius of the quarter circle.Let r be radius of the inscribed circle.R is;√(3²+4²)R=√(25)R= 5 units.Again, R is the radius of the ascribed quarter circle.Therefore r is;(5-r)²=(3+r)²+r²25-10r+r²=9+6r+r²+r²r²+16r-16=0Using quadratic equation app to resolve the quadratic equation above.Therefore;r = 0.94427 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3533495

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Calculating Area yellow circle : Area red semi circle.Let the radius of the bigger circle be 2 unit.Therefore the radius of the smaller circle will be;½(2)=1 unit.Let the radius of the semi circle be r.It implies;2² + r² = (1 + r)²4 + r² = 1 +2r + r²4-1=2r2r=3Therefore r (semi circle's radius) is;r=1.5 unit.Therefore;Area yellow circle : Area red semi circle is;(1)²π : ½(1.5)²π= 1 : ½(9/4)= 1 : (9/8)= 8 : 9= 8/9

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3532497

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Calculating Shaded/Green Area.Shaded/green area is;Area semi circle of radius 9 units - 2(area sector of radius 9 units and angle 60°) + area equilateral triangle of single side length 9 units - area sector of radius 9 units and angle 50° - area quarter circle of radius 9 units + 2(area sector of radius 9 units and angle 60°) - area equilateral triangle of single side length 9 units. = ½(81π) - ⅓(81π) + ¼(81√(3)) - ¼(45π) - ¼(81π) + ⅓(81π) - ¼(81√(3))= ½(81π) - ¼(45π) - ¼(81π) = ¼(162π - 45π -...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3531515

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Calculating Area Blue.Area Blue is;Area triangle with height 4 cm and base (4sin150) cm= ½*4*(4sin150)= 2(4sin150)= 8sin150= ½(8)= 4 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3530549

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Sir Mike Ambrose is the author of the question.Calculating Area R Exactly.Area R Exactly is;Area semi circle of radius 2 unit - Area right-angled triangle of height 2√(2+√(2)) unit and width 2√(2-√(2)) unit - Area sector of radius 2 unit and angle 45° + Area isosceles triangle of two equal length, 2 unit each and angle 45° - Area quarter circle of radius 2 unit + Area isosceles right-angled triangle of height and width 2 unit respectively - Area sector of radius 2 unit and angle 22.5°.It is;½(4...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3529874

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Calculating Area Blue.Blue area is;Area square of single side length 4cm - 5(area circle of radius 1cm) + area square of single side 2cm.= 16 - 5π + 4= 20 - 5π= 5(4 - π) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3529273

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Calculating Area Blue.Notice.The ascribed plane shape is a regular octagon.Calculating it's single interior angle.na = 180(n-2)8a = 180(8-2)a = (180*6)/8a = 135°a is the single interior angle of the ascribed regular octagon.b² = 2(5²)-2(5²)cos135b = 9.23879532511 units.b is the side length of the inscribed square.Therefore, area blue is;½*9.23879532511*9.23879532511= 42.6776695296 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3528501

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Calculating Inscribed Area Blue Square.Let x be the side length of the blue square.tan60 = x/a√(3) = x/aa = ⅓(√(3)x) units b = a+xb = ⅓(√(3)x)+xb = ⅓(√(3)x+3x) units.Calculating x².10² = x²+(⅓(√(3)x+3x))²100 = x²+⅑(3x²+6√(3)x²+9x²)100 = x²+⅓(x²+2√(3)x²+3x²)300 = 3x²+x²+2√(3)x²+3x²300 = 7x²+2√(3)x²(7+2√(3))x² = 300x² = 300/(7+2√(3)) square units.x² = 28.6694463637 square units.x² is the area of the inscribed blue square.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3527473

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Calculating x (radius of the small inscribed circle)28² + x² = (56-x)²784 + x² = 3136 - 112x + x²112x = 2351x = 21 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3526250

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Calculating Area Blue.Area Blue is;Area semi circle with radius √(2) units - Area quarter circle with radius 2 units + Area triangle with height and base 2 units respectively.= ½(√(2)²)π - ¼(2²)π + ½(2²)= π - π + 2= 2 square units.
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