Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3242616

Calculating Angle x. Notice. Quadrilateral ABCD is a square. Let AB equal 2 units. a = (2-y) units. b = (1+y) units. b is MQ. c = (1-y) units. Where y is the radius of the inscribed circle. Calculating y. (1+y)² = (1-y)²+(2-y)² 1+2y+y² = 1-2y+y²+4-4y+y² 4y = 4-4y+y² y²-8y+4 = 0 (y-4)² = -4+(-4)² (y-4)² = 12 y = 4±√(12) Therefore; y ≠ = (4+2√(3)) units. y = (4-2√(3)) units. y = 0.53589838486 units. Again, y is the radius of the inscribed c...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3241835

Calculating Green Inscribed Triangle. tana = 12/10 a = atan(6/5)° b = (180-atan(6/5)) b = (90+atan(⅚))° c² = 10²+12² c = √(244) c = 2√(61) cm. d = (2√(61)-x) units. It implies; 2(2√(61)-x)sin(90+atan(⅚)) = ½*12xsin(atan(6/5)) 24-1.53644255919x = 4.60932767758x 24 = 6.14577023677x x = 3.90512483796 cm. It implies; 2A = 0.5*3.90512483796*12sin(atan(6/5)) Where 2A is area green. 2A = 18 cm² It implies; A = 9 cm² Green area is; ½(2+12)*12-18-9...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3241834

Calculating Area circle ÷ Area semi circle. Let the radius of yellow circle be r. Let the radius of the blue semi circle be R. Calculating r. It implies; (4r+1)*1 = 5*1 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/3241832

Calculating yellow area. r, radius of the inscribed circle is; 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 will be; Area of the ascribed square - 4(area green rectangle) - area inscribed circle with radius 10 units. = 400 - 4(4*2) - 100π = 40...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3241157

Sir Mike Ambrose is the author of the question. Calculating Red Shaded Area ÷ Blue Shaded Area to 2 decimal places. Let the side of the regular pentagon be 1 unit. a = 360-2(108)-90 a = 54° tan72 = b/0.5 b = 1.53884176859 units. tan54 = 1.53884176859/c c = 1.11803398875 units. d = c-0.5 d = 0.61803398875 unit. (e/tan36)+(e/tan27) = d Where e is the radius of the inscribed circle. e = 0.61803398875/((1/tan36)+(1/tan27)) e = 0.18509595408 unit. f = 180-72-54 f...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3241154

Sir Mike Ambrose is the author of the question. Calculating Shaded Area ÷ Green Area to 2 decimal places. Let the side of the regular pentagon be 1 unit. a = 108-90 a = 18° b = 180-108-18 b = 54° (1/sin54) = (c/sin108) c = 1.17557050458 units. (1/sin54) = (d/sin18) d = 0.38196601125 unit. e = 1-d e = 0.61803398875 unit. f² = 0.61803398875²+1²-2*0.61803398875cos108 f = 1.3281310261 units. (1.3281310261/sin108) = (1/sing) g = 45.73230144788° h = 180-108-45.73...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3240185

Calculating Blue Area. 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/3240181

Sir Mike Ambrose is the author of the question. Calculating Shaded Area ÷ Green Area to 2 decimal places. Let the single side length of the two congruent inscribed regular pentagon be 1 unit. Area Green is; 0.5*5(1/(2tan(180/5))) = 1.72047740059 square units. Calculating Area Shaded. a = ⅕(180*3) = 108° Where a is the single interior angle of the congruent inscribed regular pentagon. b² = 2-2cos108 b = 1.61803398875 units. c = 1+b c = 2.61803398875 units. d²...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3239469

Calculating Area Triangle ABC. Let CM be x. Calculating x. x+1 ~ x+3 1 ~ 2 Cross multiply. 2x+2=x+3 x = 1 unit. Therefore, CM = 1 unit. Therefore angle C will be; 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/3239448

Calculating Area Blue Inscribed Circle. a = (x+1) units. b = (4-x) units. It implies; (x+1)² = 1²+(4-x)² Where x is the radius of the inscribed blue circle. Calculating x. x²+2x+1 = 1+16-8x+x² 10x = 16 5x = 8 x = ⅕(8) unit. x = 1.6 units. Therefore, area inscribed blue circle is; πx² = π(8/5)² = 64π/25 square units.

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