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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3223441

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Calculating Area Blue Fraction. Let the radius of inscribed blue semi circle be 2 units. Therefore the radius of the inscribed blue quarter circle will be 2 units. The length of the ascribed rectangle will be 4 units. The width of the ascribed rectangle will be; Let the width be x. x²+2²=4² x²=16-4 x = √(12) x = 2√(3) units. Area ascribed rectangle is  4*2√(2) = 8√(3) square units. Area blue is; Area quarter circle with radius 2 units + Area semi circ...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3203679

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Calculating Shaded Area Blue. a² = 4²+3² a = √(25) a = 5 units. a is the radius of the quarter circle. 5 ~ 4 3 ~ b Cross Multiply. 5b = 12 b = 2.4 units. d² = 5²+3² d = √(34) units. tane = 3/4 e = atan(¾)° f² = 4²+2.4² f = 4.66476151588 units. g = d-f g = 1.16619037897 units  tanh = 4/2.4 h = atan(5/3)° j = 180-h j = (180-atan(5/3))° Area Blue is; (0.5*2.4*1.16619037897sin(180-atan(5/3)))+(atan(3/4)π*5²÷360)-(0.5*5²sin(atan(3/4)) = 1.2+8.043763859...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3198062

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Calculating Shaded Area Blue. Notice. 8 cm is the side length of the ascribed square. Therefore; ½(8) = 4 cm is the radius of the both inscribed half circles. tana = 4/8 a = atan(½)° b = 2a b = 2atan(½)° tanc = 8/4 c = atan(2)° d = 2c d = 2atan(2)° Area Blue is; Area sector with radius 8 cm and angle 2atan(½)°-Area triangle with height 8 cm and base 8sin(2atan(½)) cm+Area sector with radius 4 cm and angle 2atan(2)°-Area triangle with height 4 cm and base 4sin...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3196265

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Calculating Shaded Fraction. Let the radius of the inscribed circle be 1 unit. Therefore, the radius of the inscribed half circle is 2 units. a² = 2²+(2+2)² a² = 20 a = 2√(5) units. a is the radius of the ascribed quarter circle. Shaded Area is; ½*π(2)²+π(1)² = 2π+π = 3π square units. Area ascribed quarter circle is; ¼*π(2√(5))² = ¼(20π) = 5π square units. Therefore, shaded fraction area is; Shaded Area ÷ Area ascribed quarter circle = 3π÷5π = ⅗

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3193643

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Calculating Area Blue. a = ½(4) a = 2 units. a is the radius of the inscribed half circle. b = (2+x) units. x is the radius of the inscribed circle. c = (4-x) units. It implies; d²+x² = (4-x)² d² = 16-8x+x²-x² d = √(16-8x) units. e = (2-x) units. Calculating x. (2+x)² = (2-x)²+√(16-8x)² 4+4x+x² = 4-4x+x²+16-8x 16x = 16 x = 1 units. Again, x is the radius of the inscribed circle. Therefore, Blue Area is; Area quarter circle with radius 4 units-Area half circle with radius 2 units-Area...

Mathematics Question and Solution

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

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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/3183735

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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/3181225

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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...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3175456

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Calculating x. Let r be the radius of the inscribed green circle. Let R be the radius of the ascribed quarter circle. (R-r)² = r²+5² --- (1). (R-r)²+5² = a² --- (2). a² = x²+r² --- (3). Equating (3) and (2). (R-r)²+5² = x²+r² (R-r)² = x²+r²-5² --- (4). Equating (4) and (1). x²+r²-5² = r²+5² x²-5² = 5² x² = 5²+5² x² = 25+25 x² = 50 x = √(50) x = 5√(2) units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3174819

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Shaded Area is; Area circle with radius 4 cm - 4(area quarter circle with radius 4 cm - area isosceles right-angled triangle with equal adjacent lengths 4 cm). = π*4²-4(¼(4²π)-½(4²)) = 16π-4(4π-8) = 16π-16π+32 = 32 square units.
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