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)....

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.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2162533

Sir Mike Ambrose is the author of the question. Notice; Side length of the congruent regular hexagon is 2 units. (a) Calculating Length Blue ÷ Length Red. Length Blue is; Let it be x. 4²=2²+x²-4xcos150 x²+2√(3)x-12= 0 It implies; x (Length Blue) = (√(15)-√(3)) units. Length Red is; Let it be y. y = √(8-8cos120)-x y = 2√(3)-(√(15)-√(3)) It implies; y (Length Red) = (3√(3)-√(15)) units. Therefore; Length Blue ÷ Length Red exactly is; (√(15)-√(3)) ÷ (3√(3)-√(15)) = ½(√(5...

Short Video of Our Teaching and Learning Activities

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Mathematics Question and Solution

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Mathematics Question and Solution

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Mathematics Question and Solution

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