Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1923083

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 unit. 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 unit. Where e is the radius of the inscribed circle. Area Lilac (inscribed circle) is; π(0.32738307374)² =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1923070

Let GD (inscribed square side) be a. Calculating a. 2(a/(tan60))+a = 12 a = 12/((2/√(3))+1) a = 5.56921938165 cm. b = ½(12-5.56921938165) b = 3.21539030918 cm. Where b is BD = CE. c = 3.21539030918+5.56921938165 c = 8.78460969083 cm. Where c is CD. d² = 3.21539030918²+12²-24*3.21539030918cos60 d = 10.75890566601 cm. Where d is AD. (10.75890566601/sin60) = (12/sine) e = 105° Where e is angle ADB. f = 105-90 f = 15° Where f is angle ADG. cos15 = 5.56921938165/g g = 5.7656801693 cm. Where...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1923013

tana = (4/3) a = atan(4/3)° b = (135-atan(4/3))° (c/sin45) = (6/(135-atan(4/3))) c = 4.28571428571 units. Therefore Area Blue is; 0.5*4.28571428571*6sin(atan(4/3)) = 10.28571428571 square units. = (72/7) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1922578

Notice; The bigger square side is 1 unit. Calculating the big square side. Let it be a. a² = 2(½)² a = (1/√(2)) units. Calculating the biggest square side. Let it be b. b² = (0.5)²+(1.5)² b = ½√(10) units. tanc = ((0.5)/(1.5)) c = atan(0.5/1.5)° d = (45-atan(0.5/1.5))° e = 90-(45-atan(0.5/1.5)) e= (45+atan(0.5/1.5))° tan(45+atan(0.5/1.5)) = d/(1/√(2)) d = √(2) units. Therefore shaded region is; ½*a*d = ½*(1/√(2))*√(2) = ½ square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1921900

Let the regular pentagon side length be 1 unit. Single interior angle of the regular pentagon is; ⅕(180*3) = 108° a = 108-90 a = 18° b = 180-18-108 b = 54° (1/sin54) = c/sin108) c = 1.17557050458 units. d = 108-36 d = 72° tan72 =e/0.5 e = 1.53884176859 units. f = 54-18 f = 36° g² = 1.53884176859²+1.17557050458²-2*1.17557050458*1.53884176859cos36 g = 0.9071653746 units. (0.9071653746/sin36) = (1.17557050458/sinh) h = 49.61382244038° j² = 1+1.53884176859²-2*1.53884176859cos54 j = 1.248...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1921452

Let the square side be a. Calculating a. a²+(0.5a)² = 4² a²+¼(a)² = 16 ¼(5a²) = 16 5a² = 64 a = 8/√(5) a = ⅕(8√(5)) units. Half a is; = ⅕(4√(5)) units. tanb = ((4/√(5))/(8/√(5))) b = atan(0.5)° c = atan(2)° d = (atan(2)-atan(0.5))° tan(atan(2)-atan(0.5)) = e/(4/√(5)) e = (3/√(5)) units. f = a-e f = (8/√(5))-(3/√(5)) f = (5/√(5)) units. It implies; Area yellow (rectangle) is; (8/√(5))*(5/√(5)) = ⅕(40) = 8 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1920365

a = 45-atan(3/4) a = 45-36.86989764584 a = 8.13010235416° Where a is angle DCF. b² = 2(5²) b = 5√(2) cm. Where b is CF = AE. c² = (5√(2))²+4²-10√(2)*4cos8.13010235416 c = 3.16227766017 cm. Where c is DF. (4/sind) = (3.16227766017/sin8.13010235416) d = 10.30484646877° Where d is angle DFC. e = 45-10.30484646877 e = 34.69515353123° Where e is angle AFD. tan34.69515353123 = f/5 f = 3.46153846154 cm. g = 90-34.69515353123 g = 55.30484646877° h = atan(5/(5-3.46153846154)) h = 72.89727103...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1919801

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

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1919754

Let the longer diagonal be 1 unit. (1/sin150) = (a/sin18) a = 0.61803398875 units. b = 12° (1/sin150) = (c/sin12) c = 0.41582338164 units. d = 180-84-42 d = 54° (e/sin54) = (0.41582338164/sin42) e = 0.50275413979 units. f² = 0.50275413979²+0.61803398875²-2*0.61803398875*0.50275413979cos66 f = 0.61803398875 units. (0.61803398875/sin66) = (0.50275413979/sing) g = 48° It implies; The required angle, theta is; 48-b = 48-12 = 36°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1919356

Notice; Triangle ABC is equilateral. Let the side of the regular pentagon be a. Single interior angle of the regular pentagon is; ⅕(180*3) = 108° (HF)² = 2a²-2a²cos108 HF = 1.61803398875a units. sin18 = b/a b = 0.30901699437a units. c = HF-b c = 1.61803398875a-0.30901699437a c = 1.30901699438a units. d = 1-c d = (1-1.30901699438a) units. cos18 =e/a e = 0.9510565163a units. Calculating a, side length of the regular pentagon. tan60 = e/d √(3) = 0.9510565163a/(1-1.30901699438a) √(3)-2.26...

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