Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2781317

Let the regular pentagon side length be 1 unit. sin72 = a/1 a = 0.9510565163 unit. Let the side length 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;...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2779791

Let a be the radius of the circle. b = 2a units. b is the diameter of the circle. Calculating a observing similar plane shape (right-angled triangle) ratios. It implies; 2a - 5 9 - a Cross Multiply. 2a² = 45 a = √(45/2) a = 3√(5)/√(2) a = ½(3√(10)) units. a = 4.7434164903 units. Again, a is the radius of the circle. Calculating the side length of the inscribed yellow square. Let it be c. 2a² = c² c² = 2(½(3√(10)))² c² = ½(90) c = √(45) c = 3√(5) units. c...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2779762

Let the radius of the ascribed half circle be a. Let the radius of the inscribed half circle be b. It implies; a² = b²+(0.5*12)² a²-b² = 6² a²-b² = 36 square units. Where (a²-b²) is the blue area.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2779739

Sir Mike Ambrose is the author of the question. Let the radius of the semi circle be 1 unit. Therefore; Area lilac is; Area triangle with height 0.26794919243 units and base 1 unit = ½(0.26794919243) = 0.13397459622 space units. Area large square is; Area square with side length 1 unit = 1² = 1 square unit. Area Lilac ÷ Area Large Square in its simplest decimal form is; 0.13397459622 ÷ 1 = 0.13397459622 ≈ 0.134 to 3 decimal places.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2779183

Let AB be 5 units. Radius, r of the inscribed circle is; 5*(2/5) r = 2 units. a = ⅛(180*6) a = 135° 2b² = 25 b = ½(5√(2)) units. c = 180-0.5(135)-45 c = 67.5° sin22.5 = ½(5√(2))/d d = 9.23879532511 units. Where d is the side length of the regular triangle (purple area). Area purple is; 0.5*9.23879532511*9.23879532511sin60 = 36.95994598698 square units. Calculating Area Shaded. e = 360-135-45-67.5-60 e = 52.5° f² = 50-50cos135 f = 9.23879532511 units...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2778301

Shaded inscribed area is; Area regular hexagon with side 1 unit - 6(Area sector with radius 1 unit and angle 60°) + 6(Area equilateral triangle with side 1 unit). = 6/(4tan(180÷6)) - 6(60π÷360) + 6*½(sin60) = (3√(3)/2) - 6(π/6) + 6*¼(√(3)) = ½(3√(3)) - π + ½(3√(3)) = (3√(3)-π) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2778284

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

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2777592

Sir Mike Ambrose is the author of the question. 18² = 14²+16²-2*14*16cosa 448cosa = 14²+16²-18² a = acos((14²+16²-18²)/448) a = 73.39845040098° (18/sin73.39845040098) = (14/sinb) b = 48.18968510422° c = 180-48.18968510422-73.39845040098 c = 58.4118644948° cotd = cota+cotb+cotc cotd = 1.80748828181 d = acot(1.80748828181) d = 28.95373454979° e = 58.4118644948-d e = 29.45812994501° f = 180-28.95373454979-73.39845040098 f = 77.64781504923° (14/sin77.64781504923) = (...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2776792

Green Area is; 2(area square with side 2 cm - area quarter circle with radius 2 cm) + 3(area sector with radius 1 unit and angle 300°) + 4(area equilateral triangle with side 1 unit) = 2(4 - ¼(4π)) + 3(300π÷360) + 4(½sin60) = 8 - 2π + ½(5π) + √(3) = ½(16-4π+5π+2√(3)) = ½(16+π+2√(3)) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2776777

Sir Mike Ambrose is the author of the question. a = 6-2 a = 4 units. b² = 6²-4² b = 2√(5) units. c = 6-b c = (6-2√(5)) units. d = asin(⅔)° tan(asin⅔) = e/(6-2√(5)) e = ⅕(12√(5)-20) units. f = 4+e f = ⅕(12√(5)) units. g² = 6²+(⅕(12√(5)))² g = ⅕(18√(5)) units. 6² = (⅕(18√(5)))²+(⅕(12√(5)))²-2*⅕*⅕*18*12*5cosh 36 = ⅕(468)-⅕(432)cosh ⅕(432)cosh = ⅕(468)-36 ⅕(432)cosh = ⅕(288) h = acos(288/432) h = 48.18968510422° i = 90-h i = 41.81031489578° Therefore; A...

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