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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2121779

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Let the regular hexagon side length be a. Calculating a. 0.5a²sin120 = 4√(3) √(3)a² = 16√(3) a = 4 units. b² = 4²+4²-2*4*4cos120 b = 4√(3) units. c = ½(b) c = 2√(3) units. d² = 2²+4²-2*2*4cos120 d = 2√(7) units. (2√(7)/sin120) = (2/sine) e = 19.1066053509° f = 120-e f = 100.8933946491° tan60 = 2√(3)/g g = 2 units. h² = 6²+28-24√(7)cos100.8933946491 h = 8.7177978871 units. (8.7177978871/sin100.8933946491) = (2√(7)/sinj) j = 36.5867755536° k = 120-36.5867755536 k = 83.4132244464° l =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2120814

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a² = 6²+18²-2*6*18cos150 a = 23.3893455919 cm. (23.3893455919/sin150) = (18/sinb) b = 22.6307402124° tan22.6307402124 = c/6 c = 2.5013366786 cm. Area Red exactly in decimal is; 0.5*2.5013366786*18sin60 = 19.4959899641 cm² Calculating Tanx. d² = 6²+18² d = 6√(10) cm. d = 18.973665961 cm. e² = 6²+2.5013366786² e = 6.5005142243 cm. f = 18-2.5013366786 f = 15.4986633214 cm. 15.4986633214² = 6.5005142243²+18.973665961²-2*6.5005142243*18.973665961cosg 240.2085647501 = 402.2566851799-246.67...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2120630

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Sir Mike Ambrose is the author of the question. Let the single side length of the congruent regular hexagons be 1 unit. Therefore;  Area red is; Area trapezium with two parallel side length ½(3√(3)) unit and 2√(3) unit, and height ½ unit + Area triangle with height 2√(3) unit and base 2 unit. ½*½(½(3√(3))+2√(3)) + ½(2√(3)*2) = (7√(3))/8 + 2√(3) = (23√(3)/8) square unit. Area orange is; Area trapezium with two parallel side length 1 unit and 2 unit, and height ½√(3) unit + Area trapeziu...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2120575

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sin30 = a/10 a = 5 cm. b = 10+2a b = 20 cm. c² = 20²+4²-160cos60 c = 4√(21) cm. c = 18.3303027798 cm. (18.3303027798/sin60) = (20/sind) d = asin(5√(7)/14)° d = 70.8933946491° e = 180-d e = (180-asin(5√(7)/14))° e = 109.1066053509° Where e is x. Therefore; tanx is; tan(180-asin(5√(7)/14)) tan(109.1066053509) = -2.8867513459 Calculating Blue Area. f² = 10²+10²-200cos 120 f = 10√(3) cm. g² = 10²+4²-2*10*4cos120 g = 2√(39) cm. (2√(39)/sin120) = (10/sinh) h = asin(5√(13)/26)° h = 43.897886...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2120136

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Sir Mike Ambrose is the author of the question. Let the side of square ABCD be x. Calculating x. ½*x(x+½(x)) = 84+24 ½(½(3x²)) = 108 ¼(x²) = 36 x² = 36*4 x = 12 cm. Notice; The base of blue area is; ½(x) = 6 cm. Calculating blue area height. Let it be y. ½*6*y = 24 y = 2*4 y = 8 cm. It implies; Area Green exactly is; Area triangle with height ½(3√(13)) cm and base ⅕(24)sin(atan(3/2)) cm. = ½*½(3√(13))*⅕(24)sin(atan(3/2)) = ¼(3√(13))*(72√(13)/65) = ⅕(54) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2118217

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Blue area is; 8(area quarter circle with radius 4 cm - area triangle with height and base 4 cm each) - 8(area quarter circle with radius 2 cm - area triangle with height and base 2 cm each) = 8(4π-8) - 8(π-2) = 32π-64-8π+16 = 24π-48 = 24(π-2) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2118040

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Let the red length be a. Calculating a. b² = 8²+8² b = 8√(2) units. c² = 2²+2² c = 2√(2) units  d = 8√(2)-2√(2)-2-½(a) d = ½(12√(2)-4-a) units. e² = 2a²-2a²cos120 e² = 3a² e = √(3)a units. Equating d and e to get a. ½(12√(2)-4-a) = √(3)a 12√(2)-4-a = 2√(3)a 12√(2)-4 = 2√(3)a+a (12√(2)-4) = (2√(3)+1)a a = (12√(2)-4)/(2√(3)+1) a = ((12√(2)-4)(2√(3)-1))/11 a = (24√(6)-12√(2)-8√(3)+4)/11 units. a = 2.9055258743 units. Calculating Area Purple. f = 180-120-45 f = 15° (2.9055258743)² = 2g² g...

We are smart and clever!

https://onlineedumath.com/update/we-are-smart-and-clever/2117640

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Our certified, experienced, resilient, productive and committed Math Educators will be glad to be at your service. We make teaching and learning Mathematics fun for learners, we expose the simplicity and beauty of Mathematics to our learners, and mentor them to appreciate and love Mathematics. Communicate us to mentor/educate you Mathematics better online at affordable tuition.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2116937

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Notice; The radius, a of the small inscribed circle is; a = 2 units. Calculating b, radius of the big circle. c² = 8²+8² c = √(128) c = 8√(2) units. d² = 2²+2² d = √(8) d = 2√(2) units. It implies; b = ½(c-d-a) b = ½(8√(2)-2√(2)-2) b = ½(6√(2)-2) b = (3√(2)-1) units. b = 3.2426406871 units. 2e² = (6√(2)-2)² √(2)e = 6√(2)-2 e = ½(12-2√(2)) e = (6-√(2)) units. f = 8-e f = 8-(6-√(2)) f = (2+√(2)) units. Area Green exactly is; ½(2+√(2))*6 = 3(2+√(2)) square units. = 10.2426406871 square...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2116605

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Let the regular triangle side length be 2 units. Therefore the square side length is 1 unit. a² = 2(1²) a = √(2) units. b² = 2+1-2√(2)cos105 b = √(3-2√(2)cos105) units. (√(3-2√(2)cos105)/sin105) = (√(2)/sinc) c = 45° (1/sin75) = (d/sin45) d = 0.7320508076 units. d = (√(3)-1) units. Area Blue is; 0.5*1*0.7320508076sin60 = 0.3169872981 square units. = ¼(3-√(3)) square units. Calculating Area Red. sin30 = e/1 e = ½ units. (2/sin75) = (f/sin45) f = 1.4641016151 units. f = (2√(3)-2) units...
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