Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2176051

Let BC be 1 unit. AB = 2 units. tan18 = a/2 a = 0.6498393925 units. a is the radius of the inscribed circle. Area inscribed circle is; π(0.6498393925)² = 1.3266670448 square units. b = ½(2+1) b = 1.5 units. b is the radius of the ascribed semi circle. c = 180-72 c = 108° (1.5/sin36) = (d/sin108) d = 2.4270509831 units. e = 2.4270509831-2 e = 0.4270509831 units. Calculating Area Red. It is; 0.5*0.6498393925*0.4270509831 = 0.1387572757 square units. It implies; Area Red ÷ Area Circle...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2175019

sin30 = a/12 a = 6 units. cos30 = b/12 b = 6√(3) units. Calculating k. It implies; ½(2k+6)(6√(3))+(1.5k*(6+k)) = 108+54√(3) 6√(3)k+18√(3)+9k+(3k²/2) = 108+54√(3) (3k²/2)+(6√(3)+9)k = 108+36√(3) k²+(4√(3)+6)k = 72+24√(3) Therefore; k = 6 units. Area Yellow exactly is; ½(6+9)(3√(3))+½(9*(9+3√(3))) = ½(45√(3))+½(81+27√(3)) = ½(45√(3)+27√(3)+81) = ½(72√(3)+81) square units. = (36√(3)+40.5) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2174341

Let the radius of the ascribed quarter circle be 2 units. Radius inscribed semi circle is 1 unit. Therefore; Area Semi Circle is; ½(π) square units. Calculate Area Shaded. tana = ½ a = atan(½)° b = 2a b = 2atan(½)° c = (180-4atan(½))° d² = 2²+2²-2*2*2cos(180-4atan(½)) d = 2.4 units. e = 2.4-2 e =0.4 e = 2/5 units. tanf = (2/5)/1 f = atan(2/5)° Shaded Area is; ½*⅖*1 - (πatan(2/5)/360) = ⅕-(πatan(2/5)/360) = (72-πatan(2/5))/360 square units. Therefore; Area Shaded ÷ Area Semi Circl...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2173310

Let the regular triangle side length be 1 unit. Calculating Area Purple. (1/sin105) = (a/sin60) a = 0.8965754722 units. Area Purple is; 0.5*0.8965754722*1sin45 - ½*½*½ = 0.3169872981-0.125 = 0.1919872981 square units. Calculate Green Area. sin60 = b/1 b = √(3)/2 units. ((√(3)/2)/sin135) = (0.5/sinc) c = 24.0948425521° d = 180-135-24.0948425521 d = 20.9051574479° (0.5/sin24.0948425521) = (e/sin20.9051574479) e = 0.4370160244 units. Where e is the diagonal of green area. Area Green is; ½(0...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2173305

Let the single side length of the regular octagon be 2 unit. Therefore; Area green is; Area triangle with height and base √(2) unit + Area triangle with height 2√(2) unit and base 1 unit - Area triangle with height √(2) unit and base ½ unit. = ½(√(2))² + ½(2√(2)) - ½(½*√(2)) = 1 + √(2) - ¼√(2) = ¼(4+4√(2)-√(2)) = ¼(4+3√(2)) space unit. Area blue is; Area square with side 2 unit + Area rectangle with length 2 unit and width √(2) unit - 2(Area triangle with height √(2) unit and base ½ unit)....

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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/2170806

Let the inscribed square side be 2 units. Area Orange is; 2² = 4 square units. a² = 2²+1² a = √(5) units. a is the radius of the inscribed arc. Calculate Green Area. (√(5)/sin120) = (2/sinb) b = 50.7684795164° c = 60-b c = 60-50.7684795164 c = 9.2315204836° c = 60-asin(2sin120/√(5)) Area Green is; 0.5*√(5)*2sin9.2315204836 = √(5)sin9.2315204836 = √(5)sin(60-asin(2sin120/√(5))) = 0.3587194676 square units. Therefore; Area Green ÷ Area Orange exactly in deci...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2169005

Let the radius of the semi circle be 1 unit. cos60 = a/1 a = ½ units. sin60 = b/1 b = √(3)/2 units. Where b is the side length of the square. Area Square is; (√(3)/2)² = ¾ square units. = 0.75 square units. c² = 1²+(3/4)-2*(√(3)/2)cos120 c = √(¼(2√(3)+7)) units. c = 1.6174131828 units. (1.6174131828/sin120) = (1/sind) d = 32.373659127° e = 45-d e = 45-32.373659127 e = 12.626340873° (1/sin12.626340873) = (1.6174131828/sinf) f = 20.7048110551° g = 180-135-f g = 45-20.7048110551 g = 24.29...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2166217

Sir Mike Ambrose is the author of the question. Let the radius of the congruent circles be 1 unit. Therefore a side of the regular pentagon is; 1/(2sin54) unit. It implies; Angle Alpha is; 2(asin((1/(4sin54))/1.48628965095)) = 24° Angle Beta is; 2(atan((1/(4sin54))÷ 0.27824015149 )) = 96°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2164280

Sir Mike Ambrose is the author of the question. Let Alpha be x. Calculating x; ½(180-atan2)-atan(0.5) x = ½(90-atan(0.5)) It implies; tan x exactly is; = tan(½(90-atan(0.5))) Calculating Area Orange. Notice, Area Orange is an isosceles triangle with one of the two congruent sides 1.01857603 units. It implies; Area Orange exactly in decimal is; Area triangle with height 1.01857603 units and base 1.01857603sin(atan2) units. = ½*1.01857603*1.01857603sin(atan2) = 0.46398282133 square units.

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