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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3391404

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Calculating (length Blue + length red)/(length yellow).Let r be the radius of the circle.Calculating r.πr² = 144πr² = 144r = 12 cm.a = 2ra = 24 cm.a is the diameter of the circle.Let b be the blue length.A sincere study of the plane shape derives a regular hexagon inscribing the circle with blue side length b each length.Notice.The single six interior angles of the regular hexagon is 120° each.Let c be the red length.c²+b² = 24²c = √(576-b²) units.Calculating b.√(576-b²)² = b²+b²-2*b*bcos120 57...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3391154

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Sir Mike Ambrose is the author of the question.Calculating r, radius of the circle.Radius of the circle, r is;r² = (8+(3/2))²+4²r² = (19/2)²+16r² = ¼(425)r = ½(5√(17)) cmTherefore;Area shaded, exactly in cm² decimal is;Area sector with radius ½(5√(17)) cm and angle (180-atan(8/19)-atan(16/13))° - Area triangle with height 8 cm and base 6.5 cm - Area triangle with height 8 cm and base 3.36842105263 cm -Area trapezoid with two parallel side 7.36842105263 cm and 8 cm, and height 1.5 cm= ((180-atan...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3391151

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Calculating length x.12*2 = 3(x-3)24 = 3(x-3)24 = 3x-933 = 3xx = 11 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3390247

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Sir Mike Ambrose is the author of the question. Calculating Exact Area Blue. Let the small inscribed square side length be x. The big inscribed square side length will be 2x. Calculating x. ⅓(√(3)x+2√(3)x+3x+6x) = 18+6√(3) (9+3√(3))x = 3(18+6√(3)) (3+√(3))x = 6(3+√(3)) x = 6 cm Therefore: Area Blue exactly in decimal is; Area triangle with height 12sin(atan(12/(12+4√(3))))÷sin(180-atan(12/(12+4√(3)))-atan(⅔)) cm and base 12sin(atan(⅔)) cm. = ½*12sin(atan(12/(...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3390245

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Sir Mike Ambrose is the author of the question. Calculating Area Orange ÷ Area Quadrilateral ABCD Exactly. Area Orange (trapezoid) is; Area trapezoid with parallel sides ⅔ units and ½ units, and height √(3)/6 units. = ½*(√(3)/6)(½+⅔) = 7√(3)/72 square units. Area quadrilateral ABCD is; Area trapezoid with parallel sides ⅔ units and ½ units, and height √(3)/6 units + 2(area triangle with height ⅓√(3) units and base ⅓ units + Area triangle with height (√(3)/6) units and base ½...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3389152

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Calculating r, radius of the half circle. a = 2r units. a is the diameter of the half circle. b = ½(2r-4) b = (r-2) units. c²+(r-2)² = (4√(3))² c²+r²-4r+4 = 48 c² = 44+4r-r² c = √(44+4r-r²) units. d = (r-4) units. e = b-d e = (r-2)-(r-4) e = 2 units. It implies, radius of the circle, r is; r² = 2²+√(44+4r-r²)² r² = 4+44+4r-r² 2r²-4r-48 = 0 r²-2r-24 = 0 r²-6r+4r-24 = 0 r(r-6)+4(r-6) = 0 (r-6)(r+4) = 0 It implies; r ≠ -4  r = 6 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3388285

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Calculating Red Area. a²+68² = 85² a² = 7225-4624 a = √(7225-4624) a= 51 units. Let b be the radius of the circle. Calculating b.  *68b+51b+85b* = 68*51 b = (68*51)/(68+51+85) b = 17 units. c = a-b c = 51-17 c = 34 units. tand = 68/51 d = atan(68/51)° d = 53.1301023542° It implies; Red Area is; ½(68*51)-½(34²sin(53.1301023542) = 1271.6 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3388276

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Sir Mike Ambrose is the author of the question. Calculating Purple Area ÷ Yellow Area. Let the side of the regular pentagon be 1 unit. Therefore; Area purple is; Area trapezium with two parallel side 0.07294901687 units and 0.38196601125 units, and height cos18 units. = 0.5*cos18*(0.07294901687+0.38196601125) = 0.21632495093 square units. Area yellow is; Area trapezium with two parallel side 0.27345747199 units and 1 unit, and height 1 unit - Area triangle with height...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3386716

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Calculating b/a. Let x be the side length of the square. Therefore; a+b = x  c² = 15²+8² c² = 225+64 c = √(289) c = 17 units. d²+x² = 17² d = √(289-x²) units. e = x-d e = (x-√(289-x²)) units. b²+x² = 15² b = √(225-x²) units. Recall. a+b = x And b = √(225-x²) units. a = (x-√(225-x²)) units. cosy = x/15 --- (2). cosy = (x-√(225-x²))/8 --- (3). Equating (2) and (3). x/15 = (x-√(225-x²))/8 8x = 15(x-√(225-x²)) 8x = 15x-15√(225-x²) 15√(225-x²) = 7...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3386713

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Sir Mike Ambrose is the author of the question. Calculating the exact shaded area. Notice; Square side is 4 units. Small regular hexagon side is 2 units. Big regular hexagon side is 4 units. Therefore; Area shaded, exactly in square unit decimal is; Area square with side 4 units - Half area small regular hexagon + Area triangle with height 2.53589838486 units and base 4√(3) units + Area triangle with height 4 units and base 4sin60 units. = 4² - ½(6√(3)) + ½(2.53589838486*4√(3)) + ½(4*...
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