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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2640118

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Calculating r, radius of the inscribed circle. r²=(r-4)²+(r-2)² r²=r²-8r+16+r²-4r+4 r²-12r+20=0 (r-6)²=-20+36 r = 6±√(16) r = 6±4 Therefore; r ≠ 2 units. r = 10 units. Therefore, area of the ascribed square is; (2r)² = (2*10)² = 20*20 = 400 square units. It implies; Yellow region area is; Area of the ascribed square - 4(area green rectangle) - area inscribed circle with radius 10 units. = 400 - 4(4*2) - 100π = 400 - 32 - 100π = 368 - 100π = 4(92-25π) square u...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2638525

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Area Blue (Star) is; Area circle of radius 20 cm - 5(area triangle with two length 14.5308505601 cm and angle 108°, the angle they form) - 5(Area sector of radius 20 cm and angle 72°) + 5(area triangle with two lengths 20 cm and angle 72°, the angle they form). = 400π - 5(0.5sin(108)*14.5308505601²) - 5(72*400π÷360) + 5(0.5*400sin72) = 400π - 502.028539715 - 1256.63706143 + 951.056516295 = 449.027976576 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2638510

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Let CM be x. Calculating x. x+1 - x+3     1 - 2 Cross multiply. 2x+2=x+3 x = 1 units. Therefore, CM = 1 units. Therefore angle C is; Sin C = ½ C = 30° Calculating AB. Notice; CB = 4 units. Therefore; Tan 30 = AB/4 1/√(3) = AB/4 Therefore; AB = ⅓(4√(3)) units. It implies; Area triangle ABC is; ½(CB * AB) = ½(4*⅓(4√(3))) = ⅓(8√(3)) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2638503

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Sir Mike Ambrose is the author of the question. Notice; Side length of the congruent regular hexagon is 2 units. (a) Calculating Length Blue ÷ Length Red. Length Blue is; Let it be x. 4²=2²+x²-4xcos150 x²+2√(3)x-12= 0 It implies; x (Length Blue) = (√(15)-√(3)) units. Length Red is; Let it be y. y = √(8-8cos120)-x y = 2√(3)-(√(15)-√(3)) It implies; y (Length Red) = (3√(3)-√(15)) units. Therefore; Length Blue ÷ Length Red exactly is; (√(15)-√(3)) ÷...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2638492

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Shaded red area is; Area quarter of radius 10 units - Area sector of radius 10 units and angle 30° - Area equilateral triangle of single side length 5 units - Area sector of radius 5 units and angle 120°. = ¼(100π)-(100π)/12-¼(25√(3))-⅓(25π) = 25π - ⅓(50π) - ¼(25√(3))  = (300π-200π-75√(3))/12 = (100π-75√(3))/12 square units. = 15.3546212326 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2638488

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Radius of the circle is; 5-(√(18-18cos(180-2atan(4/3))) = 5-3.6 = 1.4 units  = (7/5) units. Therefore area of the circle is; π(7/5)² = (49/25)π square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2637501

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Sir Mike Ambrose is the author of the question. Calculating Area Orange. Radius of the circle, r is; (5-r)²=18-18cos(180-2atan(4/3)) (5-r)²=12.96 5-r=√(12.96) 5-r=3.6 Therefore; r = 1.4 units. Area orange is; Area sector with radius 1.4 units and angle atan(4/3)° - Area triangle with two lengths 1.4 units and 1.13836187945 units, and angle ½(atan(4/3))°, the angle they form. = 1.4²π(atan(4/3))/360 - ½(1.4*1.13836187945)sin(½(atan(4/3))) = 0.90874931364 - 0.3563636363...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2636519

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Let BD = x Calculating x; 5²= √(9+x²)²+√(9+(x+5)²)²-2√(9+x²)*√(9+(x+5)²)cos45 It implies; x = 1 unit. Calculating AC. AC = √(9+(x+5)²) And x = 1 It implies; AC = √(9+(1+5)²) AC = √(9+6²) AC = √(9+36) AC = √(45) AC = 3√(5) units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2636444

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Let the radius of the quarter circle be 2 units. Radius, r of the small inscribed semi circle is; (2+r)²=1+(2-r)² r = ⅔ units. Calculating angle x; ½(atan(3/4)) = 18.43494882292°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2636430

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Let Alpha be x. Calculating x; ½(180-atan2)-atan(0.5) x = ½(90-atan(0.5)) It implies; tan x exactly is; = tan(½(90-atan(0.5))) Calculating Area Orange. Notice, Area Orange is an isosceles triangle with one of the two congruent sides 1.01857603 units. It implies; Area Orange exactly in decimal is; Area triangle with height 1.01857603 units and base 1.01857603sin(atan2) units. = ½*1.01857603*1.01857603sin(atan2) = 0.46398282133 square units.
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