Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3189445

Calculating Area Inscribed Yellow Square. Let the inscribed yellow square side length be x. Calculating x. a = (8-x) units. b = (8-2x) units. It implies; 8² = (8-2x)²+(8-x)² 64 = 64-32x+4x²+64-16x+x² 5x²-48x+64 = 0 (x-⅕(24))² = -⅕(64)+(-⅕(24))² (x-⅕(24))² = (576-320)/25 x = ⅕(24)±⅕√(256) x = ⅕(24)±⅕(16) x = ⅕(24±16) It implies; x ≠ ⅕(40) units. x = ⅕(8) units. Again, x is the side length of the inscribed yellow square. Therefore, area inscribed yellow square is...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3189442

Calculating Green Area. Notice. The composite plane shape is not drawn to scale. Let x be the width of the ascribed rectangle. Therefore; x = the diameter of the inscribed small half circle, and also the radius of the inscribed quarter circle. b = (1+x) units. b is the length of the ascribed rectangle, and also the diameter of the big inscribed half circle. c = ½(b) c = ½(1+x) units. c is the radius of the big inscribed half circle. d = ½(x) units. d is the radius of the small inscribe...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3188286

Calculating Area Yellow. Let y be each of the two equal lengths that makes the length of the ascribed rectangle. Calculating Yellow Area. a = 14+18 a = 32 units. a is the width of the ascribed rectangle. b = 2y units. b is the length of the ascribed rectangle. c² = 32²+y² c = √(1024+y²) units. d² = 14²+(2y)² d = √(196+4y²) units. e² = 18²+y² e = √(324+y²) units. Therefore; √(324+y²)² = √(196+4y²)²+√(1024+y²)²-2√(1024+y²)*√(196+4y²)cosx 324 = 4y²+1220-2√(1024+...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3188284

Sir Mike Ambrose is the author of the question. Let the two equal length of the inscribed isosceles triangle (red area) be 2 units. Therefore; Area blue will be; Area triangle with lengths 1 unit and ⅔ units, and angle 60°, the angle they form. = ½(1*⅔sin60) = (√(3)/6) square units. Area red will be; 2(area triangle with height 1 unit and base √(3) units). = 2x½(1x√(3)) = √(3) square units. Area green will be; 2(area triangle with height 2 units and base ⅔(√(3)) units). = 2x½(2x⅔(√...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3186898

Calculating square area. tana = (k+2k)/k a = atan(3)° b = 90-a b = atan(⅓)° tanc = 3k/2k c = atan(3/2)° d = 180-a-c d = 180-atan(3)-atan(3/2) d = 52.1250163489° e = 180-a e = (90+atan(⅓))° f = 180-e-b f = 180-(90+atan(⅓))-atan(⅓) f = (90-2atan(⅓))° f = 53.1301023542° g = 180-f-d g = 180-(90-2atan(⅓))-52.1250163489 g = 74.7448812969° h² = (3k)²+k² h = √(10)k units. (2k/sin(53.1301023542)) = (j/sin(90+atan(⅓))) j = 2.37170824512k units. l = h-j l = 0.7...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3186821

Calculating Blue Inscribed Square Area. Let a be the side length of the inscribed blue square. b = a+½(a) b = ½(3a) units. 6² = 2c² c² = ½(36) c = √(18) c = 3√(2) units. Notice. b = c ½(3a) = 3√(2) 3a = 6√(2) a = ⅓(6√(2)) a = 2√(2) units. Therefore, area blue inscribed square is; a² = (2√(2))² = 8 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3186819

Calculating Shaded Area. Notice. The ascribed square side length is 1 unit. tana = 1/½ a = atan(2)° b = 2a b = 2atan(2)° c = b-90 c = 2atan(2)-90 c = 36.8698976458° d = 180-b d = 180-2atan(2) d = 2atan(½)° d = 53.1301023542° e = ½(180-d) e = 63.4349488229° f = e-45 f = 18.4349488229° g² = 2-2cos53.1301023542 g = 0.894427191 units. h² = 2(½)² h = 0.70710678119 units. Area shaded gold is; 2(¼(π*1²)-½(1²))-2((53.1301023542π*1²÷360)-(0.5*1²sin53.1301023542)+(36.8698976458π*(0.5)²÷360)-...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3185009

Calculating Blue Shaded Area. Let a be the radius of each of the circle with area 10 square units. Calculating a. πa² = 10 a² = 10/π a = √(10/π) units. a = 1.78412411615 units. Area Blue is; 3(area sector with radius √(10/π) units and angle 60°). = 3(60π*√(10/π)²÷360) = 3(600/360) = 3(10/6) = 5 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3185001

Calculating r, radius of the inscribed semicircle. 15² = 13²+14²-2*13*14cosa 2*13*14cosa = 13²+14²-15² cosa = (13²+14²-15²)/(2*13*13) a = 67.380135052° It implies, r is; 13r+14r = 13*14sin67.380135052 27r = 168 9r = 56 r = ⅑(56) units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3183739

Calculating Area Square. Let x be the side length of the square. a²+x² = 3² a = √(9-x²) units. b = x-a b = (x-√(9-x²)) units. Therefore; x/3 = (x-√(9-x²))/2 Cross Multiply. 2x = 3x-3√(9-x²) 3√(9-x²) = x 9(9-x²) = x² 81 = 10x² x² = 81/10 x² = 8.1 square units. Where x² is the area of the square.

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