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.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3183735

Calculating Area Blue. Let a be the side length of the ascribed quarter circle. tan30 = 2/b b = 2√(3) units. c = (a-2) units. d = (2√(3)+½(a)) d = ½(4√(3)+a) units. Calculating a. (a-2)² = (½(4√(3)+a))²+2² a²-4a+4 = ¼(48+8√(3)a+a²)+4 4a²-16a = 48+8√(3)a+a² 3a²-(16+8√(3))a-48 = 0 3a²-29.8564064606a-48 = 0 Therefore; a = 11.3605 units. Again, a is the radius of the ascribed quarter circle. (11.3605)² = e²+f² f = √(129.06096025-e²) e is the side length of the inscribed blue square....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3182303

Calculating Area Yellow, Area of The Inscribed Half Circle. 4r+3r = 4*3 7r = 12 r = ⅐(12) units. r is the radius of the inscribed yellow half circle. Area Yellow Inscribed Half Circle is; ½(πr²) = ½*π(12/7)² = ½*π(144/49) = (72/49)π square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3182297

Calculating Area Green. sin30 = a/12 a = 6 units. b²+6² = 12². b = √(144-36) b √(108) b = 6√(3) units. sin60 = c/12 c = 6√(3) units. d² = 12²-(6√(3))² d = √(144-108) d = √(36) d = 6 units. Therefore, green area is; (60π*12²/360)-(30π*12²/360) = 24π-12π = 12π square units. Another Approach is; Area green is; Area trapezoid with parallel lengths 6√(3) units and 6 units, and height (6√(3)+6) units+Area second with radius 12 units and angle 30°-Area triangle with height 12 units and b...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3181225

Calculating Shaded Green Area. sin30 = a/2 a = 1 unit. (a')²+1² = 2² a' = √(4-1) a' = √(3) units. a'' = 2a' a'' = 2√(3) units. a'' is the side length of the inscribed regular triangle. b² = 2²+2²-2*2*2cos30 b² = 8-8cos30 b = 1.03527618041 units. c²+a² = b² c² = 1.03527618041²-1² c = 0.26794919243 units. d = 2c d = 2*0.26794919243 d = 0.53589838486 units. Shaded Green Area is; Area quarter circle with radius 2 units+Area equilateral triangle with side length 2√(3) units-3(area triangle...

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