Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2463750

Let the side length of the regular hexagon be 1 unit. a² = 2-2cos120 a = √(3) units. Area regular hexagon is; 2(½*sin120)+(1*√(3)) = ½√(3)+√(3) = ½(3√(3)) square units. = 2.5980762114 square units. Calculating yellow area. b² = 2(0.5)²-2(0.5)²cos120 b = ½√(3) units. c = ½(a-b) c = ½(√(3)-½√(3)) c = ¼√(3) units. cos60 = d/0.5 d = ¼ units. e = c-d e = ¼√(3)-¼ e = ¼(√(3)-1) units. Area yellow is; Area regular hexagon with side length 1 unit - Area triangle...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2463652

Let the inscribed semi circle's radius be a. b = 2+1 b = 3 units. b is the diameter of the ascribed semi circle. c = ½(b) c = ½(3) c = (3/2) units. c = 1.5 units. c is the radius of the ascribed semi circle. Therefore; d² = a²+(1.5-1)² d² = a²+(½)² d = √(a²+¼) units. It implies; (3/2)² = d²+a² (9/4) = √(a²+¼)²+a² (9/4) = a²+¼+a² 2 = 2a² a² = 1 a = 1 unit. Again, a is the radius of the inscribed semi circle. Diameter CD of the inscribed semi circle, let it be...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2463456

a²sin60 = 8 √(3)a² = 16 a = 4/(√√(3)) units. a = 3.0393427426 units. a is the side length of the big regular triangle. b²sin60 = 18 √(3)b² = 36 b = 6/(√√(3)) units. b = 4.5590141139 units. b is the side length of the biggest regular triangle. c² = 3.0393427426²+4.5590141139²-2*3.0393427426*4.5590141139cos60 c = 4.020672523 units. c is the side length of the bigger regular triangle. Area red is; ½*4.020672523²sin60 = 7 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2463379

Let the square side length be 1 unit. Therefore, the regular hexagon side length a, is; a = 5*1 a = 5 units. b² = 2(5)²-2(5)²cos120 b = 5√(3) units. Area regular hexagon is; 2(½*5*5sin120)+(5√(3)*5) = ½(25√(3))+25√(3) = ½(75√(3)) square units. Calculating the inscribed blue area. tan30 = c/1 c = ⅓√(3) units. Blue Area is; 6(area rectangle with length 1 unit and width ⅓√(3) units). = 6(1*⅓√(3)) = 2√(3) square units. Therefore, shaded fraction is; (2√(3)) ÷...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2463339

2² = a²+(3a)²-2*a*3acos60 4 = 10a²-3a² 4 = 7a² a² = 4/7 a = ⅐(2√(7)) units. a is the side length of the big equilateral triangle. b = 3a b = 3*⅐(2√(7)) b = ⅐(6√(7)) units. b is the side length of the biggest equilateral triangle. Therefore, area blue is; ½*a*bsin60 = 0.5* ⅐(2√(7))*⅐(6√(7))sin60 = ⅐(3√(3)) square units. = 0.742307489 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2462613

Let the side length of the regular pentagon be 1 unit. a² = 2-2cos108 a = 1.6180339887 units. cos18 = b/1 b = 0.9510565163 units. Area ascribed regular pentagon is; ½*sin108+½(1+1.6180339887)*0.9510565163 = 0.4755282581+1.2449491424 = 1.7204774005 square units. Calculating the inscribed yellow triangle area. c = ⅓*½sin108 = 0.1585094194 square units. d = ⅓(a) d = ⅓(1.6180339887) d = 0.5393446629 units. e² = 0.5393446629²+1-2*0.5393446629cos36 e = 0.6466951903 u...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2462263

Calculating angle x. a = ⅕*180(5-2) a = 108° a is the single interior angle of the regular pentagon. b = 108-½(180-108) b = 108-36 b = 72° c = 90-72 c = 18° d = 60+108 d = 168° e = ½(d) e = ½(168) e = 84° f = e-72 f = 84-72 f = 12° g = 180-c-f g = 180-18-12 g = 180-30 g = 150° Let the side length of the regular pentagon be 1 unit. h² = 2-2cos108 h = 1.6180339887 units. It implies; Observing Sine Rule. (1.6180339887/sin150) = (j/sin18) j = 1 uni...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2461674

x² = 8²+8²-2*8*8cos60 x² = 128-64 x² = 64 x = √(64) x = 8 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2460723

Notice! (4+2√(3)) units = 7.4641016151 units is the side length of the regular hexagon. a = ⅙*180(6-2) a = ⅙(180*4) a = 120° a is the single interior angle of the regular hexagon. b = ½(a) b = ½(120) b = 60° c = b-45 c = 60-45 c = 15° d = 180-2c d = 180-2*15 d = 150° cos15 = (0.5(4+2√(3))/e e = 3.8637033052 units. f = ½(d) f = ½(150) f = 75° Let g be the side length of the inscribed congruent squares. h = g-e h = (g-3.8637033052) units. Therefore;...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2460678

Notice! x+90 = 120 x = 120-90 x = 30° Where x is the required angle.

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