Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3246174

Calculating Area Yellow Circle. Let r be the radius of the circle. r² = 1²+a²-2acos135 r² = 1+a²+√(2)a --- (1). r² = √(7)²+a²-2√(7)acos45 r² = 7+a²-√(14)a --- (2) Calculating a. Equating (1) and (2). 1+a²+√(2)a = 7+a²-√(14)a (√(2)+√(14))a = 6 a = ½(√(14)-√(2)) units. a = 1.1637219122 units. Calculating r. Recall. At (1). r² = 1+a²+√(2)a And a = ½(√(14)-√(2)) units. r² = 1+(½(√(14)-√(2)))+√(2)(½(√(14)-√(2))) r² = 4 r = 2 units. Yellow Ascribe...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3245351

Sir Mike Ambrose is the author of the question. Calculating Gold Area ÷ Purple Area to 2 decimal places. Let the side of the regular decagon which is equal the side of the regular octagon be 1 unit. Calculating Area Gold. a = ⅛(180*6) a = 135° b = ½(360-2(135)) b = 45° sin45 = c/1 c = ½(√(2)) units. d = 1+2c d = (1+√(2)) units. Area Gold is; Area regular octagon with side 1 unit - Area trapezoid with parallel sides 1 unit and (1+√(2)) units and height ½(√(2)) unit...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3245347

Calculating Area Blue. Let x be the radius of the ascribed quarter circle. a²+5² = x² a = √(x²-25) units. a is the diameter of the inscribed circle. b = ½(a) b = ½√(x²-25) units. b is the radius of the inscribed circle. Area Blue is; Area quarter circle with radius x units - Area circle with radius ½√(x²-25) units. = ¼(x)²π-(½√(x²-25))²π = ¼(πx²)-(¼(πx²)-¼(25π)) = ¼(25π) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3245344

Let the width of the square be x. Therefore the length of the square is 2x. Calculating x. x² + x² = (2√(3²+3²)+2(3))² 2x² = (2√(18)+6)² 2x² = (6√(2)+6)² 2x² = 72+72√(2)+36 x² = 54+36√(2) x (rectangle width) = √(54+36√(2)) units. Therefore the length of the rectangle 2x is; = 2√(54+36√(2)) units. Therefore area of the rectangle is; 2√(54+36√(2)) * √(54+36√(2)) = 2(54+36√(2)) = 36(3+2√(2)) square units. = 209.823376491 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3244508

Sir Mike Ambrose is the author of the question. Calculating Yellow Area ÷ Area ABC. Let the single side length of triangle ABC be 2 units. Calculating Area ABC. ½(4sin60) = √(3) square units. Calculating Area Yellow. It is; Area equilateral triangle with side 2 units - Area triangle with two lengths 2 units and (√(2)/sin75) units, and angle 60°, the angle they form - Area triangle with two lengths 1 unit and (1/sin105) units, and angle 15°, the angle they form. = √(3...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3244501

Sir Mike Ambrose is the author of the question. Calculating Area Red ÷ Area Square Exactly. Let the single side length of the square be 2 units. Therefore; Area square is; 2 x 2 = 4 square units. Calculating Red Area. It will be; ½(area square with single side length 2 units) - Area triangle with base 2(2-√(3)) units and height 2 units - Area sector with radius 2 units and angle 30°. = ½(4) - ½(2*2(2-√(3)) - (4π/12) = 2 - 4 + 2√(3) - (π/3) = ⅓(6-12+6√(3)-π)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3244258

Calculating Shared Area. a = 7-½(10) a = 2 cm. b = ½(10)-r b = (5-r) cm. Where r is the radius of the inscribed circle. Calculating r. (5-r)² = r²+2² 25-10r = 4 10r = 21 r = 2.1 cm. Again, r is the radius of the inscribed circle. Shaded area pink is; ½(5²π) - 2.1²π = 12.5π - 4.41π = 8.09π cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3243665

Calculating area x and y. a = 16-4 a = 12 units. tanb = 4/12 b = atan(⅓)° c = 90-b c = atan(3)° d = 180-45-atan(⅓) d = (45+atan(3))° It implies; (e/sin45) = (12/sin(45+atan(3))) e = 9.48683298051 units (f/sin(atan(1/3))) = (12/sin(45+atan(3))) f = 4.24264068712 units. Area x is; ½*4*4.24264068712sin45 = 6 square units. Area y is; ½*12*9.48683298051sin(atan(3)) = 54 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3243662

Calculating Length EF (x). Let a be the radius of the inscribed blue half circle. b = (4+a) units. Calculating a. 8²+a² = (4+a)² 64+a² = 16+8a+a² 48 = 8a a = 6 units. Again, a is the radius of the blue inscribed half circle. c = 2a c = 2(6) c = 12 units. c is BC, the diameter of the blue inscribed half circle. d = AB+BC+CD d = 4+12+9 d = 25 units. d is AD, the diameter of the ascribed half circle. cose = 8/10 e = acos(4/5)° f = (8+x) units. Calculating x....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3242621

Calculating Pink Shaded Area. It is; Area sector with radius 12 units and angle 30°-Area triangle with height 6 units and base 6sin120 units-Area sector with radius 6 units and angle 60°+Area triangle with height 6 units and base 6sin60 units. = (30π*12²/360)-(½*6²sin120)-(60π*6²/360)+(½*6²sin60) = 12π-9√(3)-6π+9√(3) = 6π square units. Or Shaded pink area is; ½(area sector with radius 12 units and angle 30°) = ½(30π*12²/360) = ½(12π) = 6π square units.

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