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Mathematics Question and Solution.

https://onlineedumath.com/update/mathematics-question-and-solution/2840743

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Sir Mike Ambrose is the author of the question. Let AB be 2 unit. Therefore CD = 1 unit. It implies; Area Blue is; Area triangle with height 0.72111025509 unit and base sin(atan(3/2)) unit. = 0.5*0.72111025509sin(atan(3/2)) = 3/10 space unit. Area Green is; Area trapezoid with two parallel side (3/2) unit and 1 unit, and height ½ unit - Area triangle with height (3/2) unit and base ½ unit. = ½*½((3/2)+1) - ½*½(3/2) = (5/8) - (3/8) = ¼ space unit. Area Red is; Area...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2839130

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Sir Mike Ambrose is the author of the question. Area brown exactly in square unit decimal is; Area brown exactly in square unit decimal is; Area triangle with height 2 unit and base (1.93220910506sin(120-atan(2√(3))) unit. = (1.93220910506sin(120-atan(2√(3)))) cm² = 1.39230484541 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2839118

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Let the square side be x. x²+(x-4)² = a² a = √(2x²-8x+16) b² = 2²+(x-2)² b = √(x²-4x+8) It implies; (½(a))²+6² = b² ½(x²-4x+8)+36 = (x²-4x+8) x²-4x+8+72 = 2x²-8x+16 x²-4x-64 = 0 (x-2)² = 68 x = 2±2√(17) x = 2+2√(17) units. Area Shaded is; ½(x)² = ½(2+2√(17))² = 4(9+√(17)) square units. = 52.49242250247 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2837758

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Hexagon Area = 1 square units. Calculating the regular hexagon side length. Let it be a. (6a²)/(4tan30) = 1 3a² = 2/√(3) a² = ⅑(2√(3)) a = ⅓(√(2√(3))) unit. a = 0.6204032394 units. (b/sin30) = (0.6204032394/sin120) b = 0.35818997727 unit. Shaded region area is; 2(0.5*0.6204032394²sin120) - (0.5*0.35818997727*0.6204032394sin30) = ⅓ - (1/18) = (6-1)/18 = 5/18 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2837750

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Area blue is; Quarter the area of the square. = ¼(10)² = ¼(100) = 25 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2836358

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Let the side of the two congruent sides be a units. The small green square side will be; ⅔(a) units. The big green square side is; 2a - ⅔(a) = ⅓(4a) units. b = a-⅔(a) b = ⅓(a) units. Calculating a. 9² = a²+(⅓(a))² 81 = a²+(⅑(a²)) 81 = 10a²/9 a = 27/√(10) a = ⅒(27√(10)) units ⅔(a) = ⅕(9√(10)) units.  ⅓(4a) = ⅕(18√(10)) units. Area Green is; (⅕(9√(10)))² + (⅕(18√(10)))² = ⅕(162) + ⅕(648) = ⅕(810) = 162 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2836347

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Sir Mike Ambrose is the author of the question. Shaded area exactly in cm² is; Area triangle with height 84 cm and base 13 cm - Area triangle with height 10 cm and base 24 cm + Area triangle with height (65/12) cm and base 13 cm. = (½*13*84) - (½*10*24) + (½*13*(65/12)) = 546 - 120 + (845/24) = (13104 - 2880 + 845)/24 = 11069/24 cm² = 461.208333333 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2834884

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Radius of the circle, r is; r² = (8+(3/2))²+4² r² = (19/2)²+16 r² = ¼(425) r = ½(5√(17)) cm Therefore; Area shaded, exactly in cm² decimal is; Area sector with radius ½(5√(17)) cm and angle (180-atan(8/19)-atan(16/13))° - Area triangle with height 8 cm and base 6.5 cm - Area triangle with height 8 cm and base 3.36842105263 cm -Area trapezoid with two parallel side 7.36842105263 cm and 8 cm, and height 1.5 cm = ((180-atan(8/19)-atan(16/13))*π(2.5√(17))²÷360) - (0.5*8*6.5) - (...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2834872

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Calculating r, radius of the circle. (r/tan40)+(r/tan30) = 10 r = 3.42020143326 cm. (a/sin60) = (10/sin40) a = 13.47296355334 cm. tan40 = 3.42020143326/b b = 4.07603734548  (4.07603734548/sin50) = (c/sin80) c = 5.24005260459 cm. d = 13.47296355334-4.07603734548 d = 9.39692620786 cm. e² = 9.39692620786²+5.24005260459²-2*9.39692620786*5.24005260459cos130 e = 13.38142726359 cm. (13.38142726359/sin130) = (5.24005260459/sinf) f = 17.45618925878° g = 100-17.4561892587...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2833470

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Sir Mike Ambrose is the author of the question. Let the small inscribed square side length be x. The big inscribed square side length will be 2x. Calculating x. ⅓(√(3)x+2√(3)x+3x+6x) = 18+6√(3) (9+3√(3))x = 3(18+6√(3)) (3+√(3))x = 6(3+√(3)) x = 6 cm. Therefore: Area Blue exactly in decimal is; Area triangle with height 12sin(atan(12/(12+4√(3))))÷sin(180-atan(12/(12+4√(3)))-atan(⅔)) cm and base 12sin(atan(⅔)) cm. = ½*12sin(atan(12/(12+4√(3))))÷sin(180-atan(12/(12...
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