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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3364971

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Calculating Blue Area. Let a be the congruent inscribed side lengths each of the inscribed right-angled isosceles triangle. b = ½(2) b = 1 unit. c²+1² = a² c = √(a²-1) units. d = ½(180-45) d = ½(135) d = 67.5° tan67.5 = e/1 e = 2.4142135624 units. e = (1+√(2)) units. f = 1+e f = (2+√(2)) units. f is the radius of the ascribed quarter circle. g = f-2 g = √(2) units. Therefore, blue area is; ½*(fg) = ½*(2+√(2))*√(2) = ½(2+2√(2)) = (1+√(2)) square units. =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3358036

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Sir Mike Ambrose is the author of the question. Calculating Area Blue ÷ Area Red Exactly. 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 square 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...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3357212

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Calculating Area Green. Let r be the radius of the ascribed quarter circle. a²+1² = r² a² = r²-1 a = √(r²-1) cm. a is the diameter of the white inscribed circle. b = ½(a) b = ½√(r²-1) cm. b is the radius of the white inscribed circle. Therefore, area green is; Area ascribed quarter circle - Area inscribed white circle. ¼(r²)π-(½√(r²-1))²π = ¼(πr²)-¼(πr²)+¼(π) = ¼(π) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3356333

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Calculating Area S, Yellow Area. a = 20 units. a is the radius of the quarter circle. b = 2a b = 40 units. c²+20² = d² d = √(c²+400) units. e = 7+d e = (7+√(c²+400)) units. Calculating c. cosx = (7+√(c²+400))/40 --- (1). cosx = 20/√(c²+400) --- (2). Equating (1) and (2) to get c. (7+√(c²+400))/40 = 20/√(c²+400) Cross Multiply. 800 = 7√(c²+400)+c²+400 (400-c²)² = 49(c²+400) 160000-800c²+c⁴ = 49c²+19600 c⁴-849c²+140400 = 0 (c²-(849/2))² = -140400...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3291289

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Calculating Area Red. tana = 12/6 a = atan(2)° b = 90-a b = atan(½)° c = 180-2a c = 2atan(½)° Red area is; Area square with side 12 cm - Are ma quarter circle with radius 12 cm - 2(area triangle with height 6 cm and base 12 cm) + Area sector with radius 12 cm and angle 2atan(½)° - Area sector with radius 6 cm and answer 2atan(½)° = 12²-¼(12²π)-2(½*6*12)+(2atan(½)π*12²/360)-(2atan(½)π*12²/360) = 144-113.097335529-72+66.7652556961-16.691313924 = 8.9766062431 square un...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3273110

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Calculating red area. tana = 10/5 a = atan(2)° b = 2a b = 2atan(2)° c = 180-b c = 180-2atan(2) c = 2atan(½)° Area red is; Area sector with radius 5 units and angle 2atan(2)°-Area triangle with height 5 units and base 5sin(2atan(2)) units+Area sector with radius 10 units and angle 2atan(½)°-Area triangle with height 10 units and base 10sin(2atan(½)) units.-2(area quarter circle with radius 5 units -area triangle with height and base 5 units each). = (2atan(2)π*5²/360)-(0....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3268293

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Calculating area of the ascribed square. a = (2+r) cm. r is the radius of the circle yellow quarter circle. a is AB, the side length of the ascribed square. 2(2+r)² = b² b² = 2(4+4r+r²) b = √(8+8r+2r²) cm. b is BD. r² = c²+(½(7))² c² = r²-¼(49) c² = ¼(4r²-49) c = ½√(4r²-49) cm. d = ½(b) d = ½√(8+8r+2r²) Calculating r. It implies; c = d ½√(4r²-49) = ½√(8+8r+2r²) 4r²-49 = 8+8r+2r² 2r²-8r-57 = 0 (r-2)² = ½(57)+(-2)² (r-2)² = ½(57+8) (r-2)² = ½(65)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3253085

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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 un...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3245347

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Calculating Area Blue. Let x be the radius of the ascribed quarter circle. a²+5² = x² a = √(x²-25) units. a is the diameter of the inscribed circle. b = ½(a) b = ½√(x²-25) units. b is the radius of the inscribed circle. Area Blue is; Area quarter circle with radius x units - Area circle with radius ½√(x²-25) units. = ¼(x)²π-(½√(x²-25))²π = ¼(πx²)-(¼(πx²)-¼(25π)) = ¼(25π) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3236929

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Calculating Shaded Area. Shaded blue area is  Area quarter of radius 10 cm - Area sector of radius 10 cm and angle 30° - Area equilateral triangle of single side length 5 cm - Area sector of radius 5 cm and angle 120°. = (¼(100π))-((100π)/12)-(¼(25√(3)))-(⅓(25π)) = 25π - ⅓(50π) - ¼(25√(3))  = (300π-200π-75√(3))/12 = (100π-75√(3))/12 cm² = 15.3546212326 cm²
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