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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2792503

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Sir Mike Ambrose is the author of the question. Let the ascribed quarter circle radius be 4 units. Therefore; Area blue is; Area triangle with two side 1 unit and 3 units, and angle 2asin(1/3)° = ½*3sin(2asin(1/3)) = 0.94280904158 space units. Area red is; Area triangle with two side 1 unit and 3 units, and angle (180-2asin(1/3))° + Area triangle with two side 2 units and √(44/3) units, and angle 100.02498786° = ½*3sin(180-2asin(1/3)) + ½*2*√(44/3)sin100.02498786 = 0.942809...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2786035

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a = ½(360-90) a = ½(270) a = 135° b² = 6²+(4√(2))²-2*6*4√(3)cos135 b = 2√(29) units. b = 10.7703296143 units. 2c² = b² 2c² = (2√(29))² 2c² = 4*29 c² = 58 c = √(58) units. c is the radius of the quarter circle. Area yellow (quarter circle area) is; ¼(πc²) = ¼*π*√(58)² = ½(29π) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2776792

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Green Area is; 2(area square with side 2 cm - area quarter circle with radius 2 cm) + 3(area sector with radius 1 unit and angle 300°) + 4(area equilateral triangle with side 1 unit) = 2(4 - ¼(4π)) + 3(300π÷360) + 4(½sin60) = 8 - 2π + ½(5π) + √(3) = ½(16-4π+5π+2√(3)) = ½(16+π+2√(3)) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2771184

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Radius of the quarter circle is (2+3) = 5 units. Let a be the side length of the inscribed square. b²+3² = a² b = √(a²-9) units. c = 3+b c = (3+√(a²-9)) units. Calculating a. (3+√(a²-9))²+3² = 5² 9+6√(a²-9)+a²-9+9 = 25 9+6√(a²-9)+a² = 25 6√(a²-9) = 16-a² 36(a²-9) = (16-a²)² 36a²-324 = 256-32a²+a⁴ a⁴-68a²+580 = 0 It implies; a = √(10) units  a = 3.1622776602 units. Again, a is the side length of the inscribed square. Recall. b = √(a²-9) units And a = √(10)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2769787

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Calculating radius of the quarter circle. Let a be the radius of the quarter circle. b = ½(DE) b = 2√(2) units. c²+(2√(2))² = a² c² = a²-8 c = √(a²-8) units. d = c-BE d = (√(a²-8)-5) units. e = c-CD e = (√(a²-8)-3) units. It implies; Calculating a. 2√(2) - (√(a²-8)-5) (√(a²-8)-3) - 2√(2) Cross Multiply. 8 = (√(a²-8)-3)(√(a²-8)-5) 8 = a²-8-8√(a²-8)+15 8√(a²-8) = a²-1 64(a²-8) = a⁴-2a²+1 64a²-512 = a⁴-2a²+1 a⁴-66a²+513 = 0 Resolving the above quadratic...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2763226

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a² = 24²+7² a = 25 units. b = 7+25 b = 32 units. c² = 24²+32² c = 40 units. d = ½(c) d = 20 units. d is the radius of the quarter circle. Therefore, the required length, ? is; Let it be e. e²+20² = 25² e = √(625-400) e = √(225) e = 15 units. Again, e is the required length.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2761578

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Silver area is; 2(area rectangle with length 6 cm and width 3 cm - area quarter circle with radius 3 cm - area sector with radius 6 cm and angle 30° + area sector with radius 6 cm and angle 60° - area triangle with two length 6 cm each, and angle 60°). = 2((6*3)-¼(9π)-(30*36π÷360)+(60*36π÷360)-½(36sin60)) = 2(18-(9π/4)-3π+6π-9√(3)) = 2(18+(3π/4)-9√(3)) = (36+(3π/2)-18√(3)) cm² = 9.53547444414 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2755522

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Sir Mike Ambrose is the author of the question. Let the side length of the square be 10 units. Area square is; 10² = 100 square units. Therefore; Area R is; Area semi circle with radius 5 units - Area sector with radius 5 units and angle (180-2atan(2))° - Area kite with diagonal lengths √(10²+5²) units and √(200-200cos(2atan(½))) units + Area sector with radius 10 units and angle 2atan(½)° - 2(area quarter circle with radius 5 units - area triangle with height and base 5 unit...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2753144

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Blue Area is; Area square of single side 4cm - 2(area circle of radius 1cm) - 8(area square of single side 1cm) + 8(area quarter circle of radius 1cm). = 16 - 2π - 8 + ¼(8π) = 8 - 2π + 2π = 8 cm².

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2753110

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Shaded area is; Area circle with radius 1 units - 8(area quarter circle with radius 1 units - area triangle with height and base 1 units each). = π - 8(¼(π)-½) = π - 2π + 4 = (4-π) square units.
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