Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2640146

Sir Mike Ambrose is the author of the question. Let the side of the regular quadrilateral (square) be 4 units. Area square is; 4² = 16 square units. Area Red is; Area triangle with height 4.56295238924 units and base 3.14062240575sin46.50530982298 units - Area triangle with height 1.46815433032 units and base 3.14062240575sin46.50530982298 units. = 5.19860210712 - 1.6724847454 = 3.52611736172 square units. It implies; Area Red ÷ Area Square to 2 decimal places is;...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2640138

Let the radius of yellow circle be r. Let the radius of the blue semi circle be R. Calculating r. (4r+1)x1=5x1 4r+1=5 4r = 4 r = 1 unit. Calculating R. 2²+3²=R² R = √(4+9) R = √(13) units. Therefore; Area circle ÷ Area semi circle is; π(1)² ÷ ½π√(13)² = π ÷½(13π) = 1 ÷ ½(13) = 2/13

Mathematics Question and Solution

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

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

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

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

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

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

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/2638476

Red shaded area will be; Area square with single side length 3 inches = 3 * 3 = 9 square inches.

Mathematics Question and Solution

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

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...

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