Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3254211

Calculating Area Square. Let x be the side length of the square. a²+x² = 13² a = √(169-x²) cm b = x-a b = (x-√(169-x²)) cm. c² = 2x² c = √(2)x c is the diagonal of the square. Calculating x², area of the square. x² = 3(½(x)√(169-x²)) 2x² = 3x√(169-x²) 2x = 3√(169-x²) 4x² = 9(169-x²) 4x²+9x² = 9*169 13x² = 9*169 x² = 9*13 x² = 117 cm² Again, x² is the area of the square.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3254203

Calculating Area Shaded. a = (x+6) cm. a is the radius of the ascribed circle. b = a-8 b = (x+6)-8 b = (x-2) cm. c = b+a c = (x-2)+(x+6) c = (2x+4) cm. c is the diameter of the inscribed circle. d = ½(c) d = (x+2) cm. d is the radius of the inscribed circle. e = d-b e = (x+2)-(x-2) e = 4 cm. Calculating x. x²+4² = (x+2)² x² +16 = x²+4x+4 12 = 4x x = 3 cm. Recall. d = (x+2) cm. Where d = r, radius of the inscribed circle. And x = 3 cm. d = r = 3+2 r...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3253085

Sir Mike Ambrose is the author of the question. Let the side length of the square be 10 units. Area square is; 10² = 100 square units. Therefore; Area R is; Area semi circle with radius 5 units - Area sector with radius 5 units and angle (180-2atan(2))° - Area kite with diagonal lengths √(10²+5²) units and √(200-200cos(2atan(½))) units + Area sector with radius 10 units and angle 2atan(½)° - 2(area quarter circle with radius 5 units - area triangle with height and base 5 un...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3253081

Calculating Area Blue. a = √(9) a = 3 units. a is the side length of the big square. b = √(16) b = 4 units. b is the side length of the bigger square. It implies; ½*3*4sinx = 3 12sinx = 6 sinx = ½ x = 30° y = 180-x y = 150° z = 360-90-90-150 z = 30° Therefore, area shaded blue is; ½*3*4sinz = ½*12sin30 = ¼*12 = 3 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3253079

x/y = golden ratio (½(1+√(5)). Therefore, the prove. Let the side length of the regular pentagon be 1 unit. a = ⅕*180(5-2) a = 108° a is the single interior angle of the regular pentagon. b = 108-90 b = 18° c = 180-108-18 c = 180-126 c = 54° Calculating y. (y/sin18) = (1/sin54) y = (sin18)÷(sin54) y = ½(3-√(5)) units. It implies; x = 1-y x = 1-½(3-√(5)) x = ½(2-3+√(5)) x = ½(√(5)-1) units. Therefore, x/y (golden ratio) is; ½(√(5)-1)÷½(3-√(5)) = (√(5)-...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3253069

Sir Mike Ambrose is the author of the question. Calculating Red Area ÷ Area ABCD Exactly. Let the side length of the regular dodecagon be 1 unit. Therefore; The side length square ABCD is; 1 + 2cos30 = (1+√(3)) units. Area square ABCD is; (1+√(3))² = 2(2+√(3)) square units. Area red is; Area triangle with two side 1 unit and ½(1+√(3)), and angle 60° = ½(1*½(1+√(3)))sin60° = (3+√(3))/8 square units. Therefore; Area red ÷ Area square ABCD is; (3+...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3250380

Calculating red area, area regular hexagon. Let x be the side length of the red regular hexagon. a² = 2x²-2x²cos120 a² = 3x² a = √(3)x units. b²+3² = x² b = √(x²-9) units. sinc = √(x²-9)/x --- (1). sinc = 5/√(3)x --- (2). Calculating x. Equating (1) and (2). √(x²-9)/x = 5/√(3)x Cross Multiply. 5x = x√(3x²-27x) 5 = √(3x²-27) 25+27 = 3x² 52 = 3x² x² = 52/3 x = √(52/3) x = 2√(13)/√(3) x = ⅓(2√(39)) units. x = 4.16333199893 units. Again, x i...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3250371

Calculating the radius of the ascribed half circle. Let r be the radius of the semi circle. Therefore; A right-angled triangle with hypotenuse 6 units, and adjacent height and base, (r-7) units and √(r²-49) units respectively is derived. It implies; 6²=(r-7)²+√(r²-49)² 36=r²-14r+49+r²-49 2r²-14r-36=0 r²-7r-18=0 (r-(7/2))²=18+(7/2)² (r-(7/2))²=(121/4) r = (7/2)±(11/2) r = ½(7±11) Therefore; r ≠ ½(-4) ≠ -2 units. r = ½(18) = 9 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3249646

Calculating Area Blue. It implies; A1 = 64π cm², therefore radius A1, x = 8 cm. A2 = 32π cm², therefore radius A1, y = 4√(2) cm. A3 = (16/3)π cm², therefore radius A1, z = 4/√(3) cm. Therefore; Area blue is; Area triangle with two length 10.3094010768 cm and 7.96625532625 cm, and angle 95.85811003° - Area sector with radius (4/√(3)) cm and angle 95.85811003° - Area sector with radius 4√(2) cm and angle 48.6724043189° -Area sector with radius 8 cm and angle 35.4694856511°....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3249575

Sir Mike Ambrose is the author of the question. Calculating Area yellow ÷ Area green. Let the side length of the regular hexagon be 1 unit. Therefore; Area green is; Area triangle with height 1 unit and base ⅓√(3) units. = ½(⅓√(3)*1) = √(3)/6 square units. Area yellow is; Area triangle with two length 0.40929915222 units and 1 units, and angle (90-atan(⅓(2√(3))))° = ½(0.40929915222*1)sin(90-atan(⅓(2√(3)))) = 0.13397459621 square units. It implies; Area yel...

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