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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2885685

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Let the side length if the regular hexagon be 1 unit. Therefore the side length of the square, y is; ½+1+½ y = 2 units. It implies; The yellow shaded angle, x is; (180 - 2atan(2-√(3)))° x = (180-30)° x = 150°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2883975

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Let the side of the regular pentagon be 1 unit. a = 108-90 a = 18° b = 180-108-18 b = 54° (1/sin54) = (c/sin108) c = 1.17557050458 units. (1/sin54) = (d/sin18) d = 0.38196601125 units. e = 1-d e = 0.61803398875 units. f² = 0.61803398875²+1²-2*0.61803398875cos108 f = 1.3281310261 units. (1.3281310261/sin108) = (1/sing) g = 45.73230144788° h = 180-108-45.73230144788 h = 26.26769855212°  I = 180-72-45.73230144788 i = 62.26769855212° (0.61803398875/sin62.26...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2882250

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Notice; The diameter of the semicircle is 8 units. Therefore radius is 4 units. tan30 = a/2 a = ⅔(√(3)) units. b = 3a b = 2√(3) units. c² = 2²+(⅔(√(3)))² c = (4/√(3)) units. d = (2/√(3))+c d = 2√(3) units. e² = 4²+4²-2*4*4cos120 e = 4√(3) units. f = atan((4/√(3))/2) f = atan(2/√(3)° g² = 4²+4²-2*4*4cos(180-2atan(2/√(3))) g = (8√(21)/7) units. h = (atan(2/√(3))-30)° Area Maroon exactly in square units is; Area triangle with height (8√(21)/7) units and...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2881669

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Let the inscribed regular pentagon side be 1 unit. Area small/inscribed pentagon is; 0.5*5(1/(2tan(180/5))) = 1.72047740059 square units. Calculating Shaded Area. a² = 2-2cos(60+108) a = 1.98904379074 units. b = ½(180-108-60) b = 6° c = 60-2(6) c = 48°   sin60 = d/1 d = 0.86602540378 units. tan24 = e/0.86602540378 = 0.38557935197 units. f = 2e f = 0.77115870394 units. g = 0.5(1-f) g = 0.11442064803 units. cos24 = 0.86602540378/h h = 0.94798282509 units...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2880549

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Let the side of the regular pentagon be 1 unit. a = 360-2(108)-90 a = 54° tan72 = b/0.5 b = 1.53884176859 units. tan54 = 1.53884176859/c c = 1.11803398875 units. d = c-0.5 d = 0.61803398875 unit. (e/tan36)+(e/tan27) = d Where e is the radius of the inscribed circle. e = 0.61803398875/((1/tan36)+(1/tan27)) e = 0.18509595408 unit. f = 180-72-54 f = 54° Therefore; g = d = 0.61803398875 unit. Shaded Area Red is; Area triangle with height 0.61803398875 units a...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2879518

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Let the single side length of the two congruent inscribed regular pentagon be 1 unit. Area Green is; 0.5*5(1/(2tan(180/5))) = 1.72047740059 square units. Calculating Area Shaded. a = ⅕(180*3) = 108° Where a is the single interior angle of the congruent inscribed regular pentagon. b² = 2-2cos108 b = 1.61803398875 units. c = 1+b c = 2.61803398875 units. d² = 2.61803398875²+1²-2*1*2.61803398875cos72 d = 2.49721204096 units. Where d is the radius of the inscribed a...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2879164

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Let the side of the regular decagon which is equal the side of the regular octagon be 1 unit. Calculating Area Gold. a = ⅛(180*6) a = 135° b = ½(360-2(135)) b = 45° sin45 = c/1 c = ½(√(2)) units. d = 1+2c d = (1+√(2)) units. Area Gold is; Area regular octagon with side 1 unit - Area trapezoid with parallel sides 1 unit and (1+√(2)) units, and height ½(√(2)) units. = ½(8*1)*(1/(2tan(180/8))-0.5(1+1+√(2))*(√(2)/2) = 4.82842712475-1.20710678119  = 3.62132034356 squa...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2877631

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Let the side of the regular hexagon which is equal the side of the square be 1 unit. a = ½(180-108) a = 36° tan36 = b/0.5 b = 0.363271264 units. Area Blue is; 0.5*0.363271264*0.5 = 0.090817816 square units. c² = 2-2cos120 c = 1.73205080757 units. d = c-1 d = 0.73205080757 unit. sin54 = e/f f = 1.2360679775e It implies; f+e = d 1.2360679775e+e = 0.73205080757 e = 0.32738307374 units. Where e is the radius of the inscribed circle. Area Lilac (inscribed cir...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2877556

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Let the regular pentagon side be 1 unit. sin72 = a/1 a = 0.9510565163 units. Let the side of the two inscribed congruent squares be b. c = ½(b) units. b+½(b) = 0.9510565163 b = 0.63403767753 units. Area Yellow is; (0.63403767753)² = 0.40200377653 square units. Calculating Area Blue. d = ½(1-0.63403767753) d = 0.18298116124 units. e² = 2-2cos108 e = 1.61803398875 units. f = ½(1.61803398875-0.63403767753) f = 0.49199815561 units. Area Blue is; 0.5(0.491...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2876028

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Let the side of the regular pentagon be 1 unit. a² = 2-2cos108 a = 1.61803398875 units. sin30 = b/0.5 b = 0.25 unit. c = 2b c = 0.5 unit. Where c is the inscribed square side. Area Square is; (0.5)² = 0.25 square units. Inscribed circle radius d is; d = ½(b) d = 0.125 unit. e = 0.5-0.125 e = 0.375 unit. f = 2atan(0.125/0.375) f = 36.86989764584° tan36.86989764584 = g/0.5 g = 0.375 unit. Shaded Area is; 0.5*0.375*0.5-π*0.125*0.125 = 0.0446626...
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