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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2749327

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Let the side length of the regular hexagon be 1 unit. It implies; x+y = 1 a = ⅙*180(6-2) a = 120° a is the single interior angle of the regular hexagon. b = 360-2a-45 b = 360-285 b = 75° c² = 2-2cos120 c = √(3) units. d = 45-30 d = 15° e = 180-15-75 e = 90° Calculating y. tan75 = √(3)/y y = 0.4641016151 units. Calculating x. Recall. x+y = 1 And y = 0.4641016151 units. x = 1-0.4641016151 x = 0.5358983849 units. Therefore; x : y is; 0.535898...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2748466

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Let the side length of the inscribed square be a. b² = 2a² b = √(2)a cm. b is the diagonal of the inscribed square. c²+a² = (4+6)² c = √(100-a²) cm. d = c-a d = (√(100-a²)-a) cm. 14² = 6²+(4+6)²-2*6*10cose 196 = 136-120cose 120cose = -60 e = acos(-½) e = 120° f = 180-e f = 60° Calculating a. tan60 = a/(√(100-a²)-a) √(3)(√(100-a²)-a) = a √(3(100-a²))-√(3)a = a √(300-3a²) = a+√(3)a 300-3a² = a²+2√(3)a²+3a² 300 = 7a²+2√(3)a² (7+2√(3))a² = 300 a² = 28.66944636...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2747739

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a = (4-b) m. Calculating b. 3 - 5 b - (4-b) Cross Multiply. 3(4-b) = 5b 12-3b = 5b 8b = 12 b = 1.5 m. Recall. a = (4-b) And b = 1.5 m. a= 4-1.5 a= 2.5 m. c = √(3²+1.5²)+√(5²+2.5²) c = 4√(5) m. c = 8.94427191 m. Therefore, the required length, x is; 4²+x² = (4√(5))² 16+x² = 80 x² = 80-16 x² = 64 x = 8 m.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2747709

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Let the side length of the regular octagon be 1 unit. a = ⅛*180(8-2) a = 135° a is the side length of the regular octagon. 2b² = 1² b = √(1/2) units. b = ½√(2) units. c = 1+b c = (1+½√(2)) units. c is the side length of the square. Therefore, alpha, let it be d, is; tand = b/c d = atan(½√(2)/(1+½√(2))) d = 22.5°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2747687

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Sir Mike Ambrose is the author of the question. Area Blue exactly in cm² decimal form is; Area trapezoid with two parallel side (7√(2)+14) cm and 15.3137084989 cm, and height 18.4852813742 cm. = ½((7√(2)+14)+15.3137084989)*18.4852813742 = 362.433549545 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2747682

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Area green is; Area rectangle with length 18 units and width 16 units - Area triangle with height 12 units and base 16 units - Area semi circle with radius 10 units. = (18*16) - ½(16*12) - ½(100π) = 288 - 96 - 50π = (192-50π) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2747671

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Area Blue is; Area square with side length 4 cm - Area quarter circle with radius 4 cm + 2(area square with side length 2 cm). = (4*4)-(¼*4*4π)+2(2*2) = 16-4π+8 = 24-4π = 4(6-π) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2747362

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Let a be the side length of the regular hexagon. sin30 = b/a b = ½(a) cm. c = 2b+a c = 2a cm. cos30 = d/a d = ½√(3)a cm. e = ½(162√(3)) cm² e = 81√(3) cm² e is half the area of the regular hexagon. Calculating a. ½(2a+a)*½√(3)a = 81√(3) ¼(3a²) = 81 a² = 27*4 a = 6√(3) cm. Again, a is the side length of the regular hexagon. sin30 = f/(6√(3)) f = 3√(3) cm. Let g be the radius of the inscribed circle. h = (3√(3)-g) cm. tan30 = g/(3√(3)-g) √(3)g = (3√(3)-g...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2746663

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a = ⅓(4L)-L a = ⅓(L) cm. tanb = L/(4L/3) b = atan(3/4)° 3/4 = c/(⅓(L)) c = ¼(L) cm. d = 180-45-atan(3/4) d = (45+atan(4/3))° It implies; ((4L/3)/sin(45+atan(4/3))) = (e/sin(atan(3/4))) e = 0.8081220356L cm. Calculating L. (0.5*0.8081220356L*(4L/3)sin45)-(0.5*(L/3)*(L/4) = 342/7 0.380952381L²-0.0416666667L² = 342/7 2.375L² = 342 L = 12 cm. Recall. e = 0.8081220356L And L = 12 cm. e = 0.8081220356*12 e = 9.6974644272cm. Therefore, red area exactly in dec...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2745936

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Sir Mike Ambrose is the author of the question. Let the single side length of the square be 2 units. Therefore; Area square is; 2² = 4 square units. Calculating area green. It is; Area trapezium with two parallel side length (√(2)/6) units and (√(2)/3) units, and height (√(2)/2) units. = ½((√(2)/6)+(√(2)/3))*(√(2)/2) = ½((√(2)/2)*(√(2)/2)) = ½(½) = ¼ square units. It implies; Area Green ÷ Area Square Exactly is; ¼ ÷ 4 = 1/16
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