Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2177695

Sir Mike Ambrose is the author of the question. Area Blue, in cm² to 1 d. p. is; Half area regular pentagon with side 12 cm - area triangle with height 6 cm and base 6tan24 cm - area triangle with height 12cos36 and base 12sin36 cm. = (½*(60*12)/(4tan(180/5))) - ½(6*6tan24) - ½(12cos36*12sin36) = 123.874372842 - 8.01411633555 - 34.2380345866 = 81.62222192 cm² ≈ 81.6 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2177527

Area of the shaded region is; Area quarter circle with radius 12 units - Area triangle with height and base 12 units respectively - Area quarter circle with radius 8 units + Area triangle with height and base 8 units respectively + Area quarter circle with radius 8 units - Area triangle with height and base 8 units respectively - Area quarter circle with radius 4 units + Area triangle with height and base 4 units. = ¼(144)π-½(144)-¼(64)π+½(64)+¼(64)π-½(64)-¼(16)π+½(16) = 36π-72-16π+32+...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2176726

Sir Mike Ambrose is the author of the question. (a) Exact radius of the circle is; ½√(2²+4²) = ½√(20) = ½*2√(5) units. = √(5) units. Or Cos(atan(2)) = (1/r) Where r is the radius of the circle. r = 1/cos(atan(2))) r = √(5) units. (b) Area Yellow exactly is; Area triangle with height 2 units and base 2sin(2atan2) units + Area triangle with height ⅕(8√(5)) units and base 8sin(90-asin(√(5)/5)) units - Area triangle with height ⅓(16) units and base 2√(5)sin(asin(√(5)/5)) units....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2176051

Let BC be 1 unit. AB = 2 units. tan18 = a/2 a = 0.6498393925 units. a is the radius of the inscribed circle. Area inscribed circle is; π(0.6498393925)² = 1.3266670448 square units. b = ½(2+1) b = 1.5 units. b is the radius of the ascribed semi circle. c = 180-72 c = 108° (1.5/sin36) = (d/sin108) d = 2.4270509831 units. e = 2.4270509831-2 e = 0.4270509831 units. Calculating Area Red. It is; 0.5*0.6498393925*0.4270509831 = 0.1387572757 square units. It implies; Area Red ÷ Area Circle...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2175019

sin30 = a/12 a = 6 units. cos30 = b/12 b = 6√(3) units. Calculating k. It implies; ½(2k+6)(6√(3))+(1.5k*(6+k)) = 108+54√(3) 6√(3)k+18√(3)+9k+(3k²/2) = 108+54√(3) (3k²/2)+(6√(3)+9)k = 108+36√(3) k²+(4√(3)+6)k = 72+24√(3) Therefore; k = 6 units. Area Yellow exactly is; ½(6+9)(3√(3))+½(9*(9+3√(3))) = ½(45√(3))+½(81+27√(3)) = ½(45√(3)+27√(3)+81) = ½(72√(3)+81) square units. = (36√(3)+40.5) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2174341

Let the radius of the ascribed quarter circle be 2 units. Radius inscribed semi circle is 1 unit. Therefore; Area Semi Circle is; ½(π) square units. Calculate Area Shaded. tana = ½ a = atan(½)° b = 2a b = 2atan(½)° c = (180-4atan(½))° d² = 2²+2²-2*2*2cos(180-4atan(½)) d = 2.4 units. e = 2.4-2 e =0.4 e = 2/5 units. tanf = (2/5)/1 f = atan(2/5)° Shaded Area is; ½*⅖*1 - (πatan(2/5)/360) = ⅕-(πatan(2/5)/360) = (72-πatan(2/5))/360 square units. Therefore; Area Shaded ÷ Area Semi Circl...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2173310

Let the regular triangle side length be 1 unit. Calculating Area Purple. (1/sin105) = (a/sin60) a = 0.8965754722 units. Area Purple is; 0.5*0.8965754722*1sin45 - ½*½*½ = 0.3169872981-0.125 = 0.1919872981 square units. Calculate Green Area. sin60 = b/1 b = √(3)/2 units. ((√(3)/2)/sin135) = (0.5/sinc) c = 24.0948425521° d = 180-135-24.0948425521 d = 20.9051574479° (0.5/sin24.0948425521) = (e/sin20.9051574479) e = 0.4370160244 units. Where e is the diagonal of green area. Area Green is; ½(0...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2173305

Let the single side length of the regular octagon be 2 unit. Therefore; Area green is; Area triangle with height and base √(2) unit + Area triangle with height 2√(2) unit and base 1 unit - Area triangle with height √(2) unit and base ½ unit. = ½(√(2))² + ½(2√(2)) - ½(½*√(2)) = 1 + √(2) - ¼√(2) = ¼(4+4√(2)-√(2)) = ¼(4+3√(2)) space unit. Area blue is; Area square with side 2 unit + Area rectangle with length 2 unit and width √(2) unit - 2(Area triangle with height √(2) unit and base ½ unit)....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2170806

Let the inscribed square side be 2 units. Area Orange is; 2² = 4 square units. a² = 2²+1² a = √(5) units. a is the radius of the inscribed arc. Calculate Green Area. (√(5)/sin120) = (2/sinb) b = 50.7684795164° c = 60-b c = 60-50.7684795164 c = 9.2315204836° c = 60-asin(2sin120/√(5)) Area Green is; 0.5*√(5)*2sin9.2315204836 = √(5)sin9.2315204836 = √(5)sin(60-asin(2sin120/√(5))) = 0.3587194676 square units. Therefore; Area Green ÷ Area Orange exactly in deci...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2169005

Let the radius of the semi circle be 1 unit. cos60 = a/1 a = ½ units. sin60 = b/1 b = √(3)/2 units. Where b is the side length of the square. Area Square is; (√(3)/2)² = ¾ square units. = 0.75 square units. c² = 1²+(3/4)-2*(√(3)/2)cos120 c = √(¼(2√(3)+7)) units. c = 1.6174131828 units. (1.6174131828/sin120) = (1/sind) d = 32.373659127° e = 45-d e = 45-32.373659127 e = 12.626340873° (1/sin12.626340873) = (1.6174131828/sinf) f = 20.7048110551° g = 180-135-f g = 45-20.7048110551 g = 24.29...

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