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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2088640

Let the green and purple color regular triangle side be a. b = √(4²+2²) b = 2√(5) units. c = 0.5b c = √(5) units. d = √(8²+4²) d = 4√(5) units. e = √(a²+(a/2)²) e = √(5a²/4) e = ½(√(5)a) Calculating a, side length of the green and purple regular triangle. d-c = e 4√(5)-√(5) = ½(√(5)a) 3√(5) = ½(√(5)a) 3 = ½(a) a = 6 units. sin60 = f/3 f = ½(3√(3)) units. cos60 = g/3 g = (3/2) units. h = 6-(3/2) h = (9/2) units. j = 12+(9/2) j = (33/2) units. tank = (3√(3)/2)/(33/2) k = atan(√(3)/11)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2087015

Notice; The regular hexagon side length is 4 units. a² = 8-8cos120 a = √(12) a = 2√(3) units. sin60 = b/2 b = √(3) units. c = a+b c = 3√(3) units. sin30 = d/2 d = 1 unit. e = 4+4+1 e = 9 units. tanf = 3√(3)/9 f = atan(√(3)/3)° f = 30° sin30 = 3√(3)/g g = 6√(3) units. h² = 32-32cos120 h = √(48) h = 4√(3) units. tanj = 4√(3)/2 j = atan(2√(3))° k = 180-30-atan(2√(3))-60 k = (90-atan(2√(3))° l = 180-60-(90-atan(2√(3)) l = (30+atan(2√(3)))° m = (30+atan(2√(3)))-90 m = (atan(2√(3))-60)°...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2086941

Sir Mike Ambrose is the author of the question. Let the square side be a. calculating a. b = (45-atan½) c = ½(√(2)a) units. d = ½(√(2)a)sin(45-atan½) c = ½(√(2)a)cos(45-atan½) It implies; ½*½(√(2)a)cos(45-atan½)*½(√(2)a)sin(45-atan½)+7 = ½*a*½(a) (3a²/40) + 7 = ¼(a²) 3a²+280 = 10a² 7a² = 280 a = √(40) a = 2√(10) units. Area Lilac exactly in square units is; Area triangle with height 3.4205262753 units and base ½(5√(2))sin(atan(4/7)) = 0.5*3.4205262753*½(5√(2))sin(atan(4/7)) = 3 square units....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2086935

Sir Mike Ambrose is the author of the question. Let AC = 1 unit. Area Yellow is; Area triangle with height ⅕(4√(5)) units and base ⅕(2√(5)) units - Area triangle with height 1 unit and base ½ unit. = ½*⅕(4√(5))*⅕(2√(5)) - ½*½*1 = ⅘-¼ = (11/20) square units. Area Red is; Area triangle with height (6/5) units and base ⅗ units. = ½*⅗*(6/5) = (9/25) square units. Area Red ÷ Area Yellow exactly is; (9/25) ÷ (11/20) = 36/55

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2084922

Let the side length of the regular nonagon be 1 unit. a = ⅑(180(9-2)) a = ⅑(180*7) a = 140° Area Nonagon is; 0.5*9*0.5tan(70) = ¼(9tan70) = 6.18182419377 square units. b = 540-3*140 b = 120° c = ½(b) c = 60° d = 140-60 d = 80° (e/sin30) = (1/sin50) e = 0.65270364467 units. sin80 = f/1 f = 0.98480775301 units. (1/sin20) = (g/sin80) g = 2.87938524157 units. sin80 = h/2.87938524157 h = 2.83564090981 units. j = 180-40-80 j = 60° (1/sin60) = (k/sin40) k = 0.74222719897 units. (0.74222...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2084619

Sir Mike Ambrose is the author of the question. Let the side length of the five inscribed congruent regular hexagon be 1 unit. It implies; The ascribed regular hexagon is; 2+(⅔) = ⅓(8) units. Area Green is; 2(area triangle with height ⅓ unit and base ⅓(sin60) units) + 2(area parallelogram with height ⅓√(3) unit and base ⅓(4) units) = 2(½*⅓*⅓*sin60) + 2(⅓*√(3)*⅓*4) = (√(3)/18) + (8√(3)/9) = (17√(3)/18) square units. Area Grey is; Area regular hexagon with side (8/3) unit...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2083545

a² = 6²+2² a =√(40) a = 2√(10) units. b = ½(a) b = √(10) units. c² = 6²+5² c = √(61) units. d = (atan(5/6)-atan(1/3))° tan(atan(5/6)-atan(1/3)) = e/√(10) e = 1.23741299746 units. cos(atan(5/6)-atan(1/3))= √(10)/f f = 3.39576072866 units. Area Orange is; ½(6*5)-½(6*2)*½(√(10)*1.23741299746 = 15-6-1.95652173913 = 7.04347826087 square units. Calculating Purple Area. g = 90-atan(6/5) g = 39.80557109227° h = atan(√(10)/1.23741299746) h = 68.62937773061° j = 180-39.80557109227-68.629377...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2083006

Let the green square side be 1 unit. Area Green Square is; 1² = 1 square units. Calculating the total shaded area. a² = 1²*2 a = √(2) units. a is the radius of the quarter circle. tan15 = b/1 b = (2-√(3)) units. c = 1-b c = (√(3)-1) units. cos15 = 1/d d = (√(6)-√(2)) units. tan30 = e/√(2) e = ⅓(√(6)) units. Shaded Area is; Area sector with radius √(2) units and angle 30° - Area with height (√(6)-√(2)) units and base (√(3)-1)sin105 units + Area triangle with height ⅓(√(6)) units and ba...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2082617

Sir Mike Ambrose is the author of the question. Let the side of the regular pentagon be 1 unit. It implies; Radius large circle, R is; = 0.580673 unit. Radius small circle, r is; = 0.168821 unit. (a) Radius Small Circle ÷ Radius Large Circle to 3 decimal places is; 0.168821 ÷ 0.580673 = 0.29073333873 ≈ 0.291 Calculating pentagon area. ½(5)*(1/(2tan(180/5))) = 1.72047740059 square units. Shaded Area is; Area triangle with height 1 unit and sin108 units - Area circle with radius 0.16882...

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