Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3207702

Calculating yellow area. Notice. Area of the ascribed square is 12 square units. Area yellow is; ½(12) - (½(⅔√(3))²sin(atan(3))÷sin(135-atan(3)))sin(45) = 6 - (½) = ½(12-1) = ½(11) square units. = 5.5 square units. Or Calculating Yellow Area. Let a be the side length of the square. a² = 12 a = √(12) = 2√(3) units. a = 3x x = ⅓(2√(3)) units. x = 1.15470053838 units. tanb = 3x/x b = atan(3)° b = 71.5650511771° c = 180-45-b c = 180-45-71.5650511771...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3207671

Calculating Area Red. Area red is; ½(3*4) - (atan(4/3)*9π÷ 360) - (atan(3/4)*4π÷ 360) = 0.54016930141 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3206769

Calculating Area Rectangle. Let r be the radius of the half circle and also, the width of the rectangle. a = r+r a = 2r units. a is the diameter of the half circle. b = (2r-x) units. b is the length of the rectangle. c = ½(6) c = 3 units. It implies; r ~ 6 3 ~ (2r-x) Cross Multiply. (2r-x)r = 18 Notice. (2r-x)r is the length times the width of the rectangle (area rectangle). Therefore; Area rectangle = 18 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3206420

Sir Mike Ambrose is the author of the question. Let the single side length of the regular hexagon be 2 units. Area rectangle is; 2.5x√(3) = ½(5√(3)) square units. Area green is; Area trapezoid with two parallel side length 3 units and height √(3) units - Area triangle with height (√(3)/3) units and base 1 unit. =½(3√(3)) - ½(√(3)/3)) = (4√(3)/3) square units. It implies; Area Green ÷ Area Rectangle exactly in its simplest form is; (4√(3)/3) ÷ ½(5√(3)) = (8√(3...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3206416

Calculating Area Green. Let x be the side length of the ascribed square. a = ½(x) units. tanb = x/(½(x)) b = atan(2)° c = 180-45-atan(2) c = (45+atan(½))° It implies; (0.5x/sin(45+atan(½))) = (d/sin(atan(2))) d = 0.47140452079x units. Calculating x. 0.5*0.47140452079x*0.5xsin45 = 12 0.47140452079a² = 48√(2) x = √(48√(2)/0.47140452079) x = 12 units. Again, x is the side length of the ascribed square. It implies; 0.5*(0.5*12)*e = 12 6e = 24 e = 4 units....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3205271

Calculating Angle x. Let AC = 1 units. sin(10+10) = a/1 a = 0.34202014333 units. a is BC. tan40 = b/0.34202014333 b = 0.28698897612 units. c = 180-10-30-40 c = 100° (1/sin100) = (d/sin10) d = 0.17632698071 units. e = a-d e = 0.34202014333-0.17632698071 e = 0.16569316262 units. Therefore, the required angle x is; tanx = e/b x = atan(0.16569316262/0.28698897612) x = 30°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3204969

Calculating Yellow Area. 2a² = 2² a = √(2) units. a is the radius of each of the two congruent half circles. 2b² = (2+1)² b² = ½(9) b = ½(3√(2)) units. b is the radius of the circle. c = a+b c = √(2)+½(3√(2)) c = ½(5√(2)) units. It implies; (½(5√(2)))² = (½(3√(2))²+d² ½(25) = ½(9)+d² 2d² = 25-9 2d² = 16 d² = 8 d = 2√(2) units. e = d-a e = 2√(2)-√(2) e = √(2) units. f = 2(d) f = 4√(2) units. Therefore, yellow area is; ½*3*4√(2)sin45 = ½(12) = 6 s...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3204947

Calculating angle x. a = 180-2(48) a = 180-96 a = 84° b = 180-72-a b = 180-72-84 b = 180-156 b = 24° c = ½(180-72) c = ½(108) c = 54° d = 90-c d = 90-54 d = 36° Therefore, the required angle x is; x+b+d = 180 x+24+36 = 180 x = 180-60 x = 120°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3204652

Calculating Area Blue. a = 5+3 a = 8 units. a is the side length of the big square. b² = 3²+8² b² = 9+64 b = √(73) units. c = ½(b) c = ½√(73) units. c is the side length of the two equal small squares. tand = (3/8) d = atan(3/8)° e = 90-45-d e = (45-atan(3/8))° e = 24.4439547804° f² = 2(½√(73))² f² = 2*¼(73) f = √(½*73) f = 6.0415229868 units. f is the diagonal of each of the two equal small squares. Area Blue is; ½*a*fsine = 0.5*8*6.0415229868sin24.443...

Mathematics Question and Solution

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

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...

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