Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3036853

Let the side of the regular pentagon be 1 unit. a = 360-2(108)-90 a = 54° tan72 = b/0.5 b = 1.53884176859 units. tan54 = 1.53884176859/c c = 1.11803398875 units. d = c-0.5 d = 0.61803398875 unit. (e/tan36)+(e/tan27) = d Where e is the radius of the inscribed circle. e = 0.61803398875/((1/tan36)+(1/tan27)) e = 0.18509595408 unit. f = 180-72-54 f = 54° Therefore; g = d = 0.61803398875 unit. Shaded Area Red is; Area triangle with height 0.61803398875 uni...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3035281

Notice; The diameter of the semicircle is 8 units. Therefore radius is 4 units. tan30 = a/2 a = ⅔(√(3)) units. b = 3a b = 2√(3) units. c² = 2²+(⅔(√(3)))² c = (4/√(3)) units. d = (2/√(3))+c d = 2√(3) units. e² = 4²+4²-2*4*4cos120 e = 4√(3) units. f = atan((4/√(3))/2) f = atan(2/√(3)° g² = 4²+4²-2*4*4cos(180-2atan(2/√(3))) g = (8√(21)/7) units. h = (atan(2/√(3))-30)° Area Maroon exactly in square units is; Area triangle with height (8√(21)/7) units and...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3033668

Let the side of the regular hexagon which is equal the side of the square be 1 unit. a = ½(180-108) a = 36° tan36 = b/0.5 b = 0.363271264 unit. Area Blue is; 0.5*0.363271264*0.5 = 0.090817816 square units. c² = 2-2cos120 c = 1.73205080757 units. d = c-1 d = 0.73205080757 unit. sin54 = e/f f = 1.2360679775e It implies; f+e = d 1.2360679775e+e = 0.73205080757 e = 0.32738307374 unit. Where e is the radius of the inscribed circle. Area Lilac (inscribed c...

Mathematics Questions and Solution

https://onlineedumath.com/update/mathematics-questions-and-solution/3032283

Sir Mike Ambrose is the author of the question. Let the side of the inscribed square be 2 units. Therefore; Area S is; Area triangle with two side 1.03528 units and 0.53589838486 units, and angle 45° = 0.5*1.03528*0.53589838486sin45 = 0.1961531464 space units. Area R is; Area triangle with two side (2√(2)-2) units and 0.65961372961 units, and angle 72.367664609° = 0.5*(2√(2)-2)*0.65961372961sin72.36766460 = 0.26038499708 space units. Area T is; Area sector with radius 2√(2) units a...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3030094

Sir Mike Ambrose is the author of the question. P coordinate is; P(3, 9) Q coordinate is; Q(2, 5), Q(3, 5) It implies; Shaded area exactly in its square units simplest form is; (Area under the curve at x = 2 and x = 3) - (Area trapezoid with parallel sides ⅓(23) units and 9 units, and height 1 unit). = (8+ln(81/16)) - ½((23/3)+9) = (8+ln(81/16))-½(50/3) = (8+ln(81/16))-⅓(25) = (ln(81/16)-⅓) square units. = 1.2885270991 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3028425

Sir Mike Ambrose is the author of the question. Calculating the circle's radius, r. 21r + 15r + 12√(2)r = 21*12√(2)sin45 (36+12√(2))r = 252 r = 252/(36+12√(2)) cm r = 3(3-√(2)) cm It implies; The exact area of the Circle in terms of π square cm is; π(9-3√(2))² = 9π(11-6√(2)) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3026716

Sir Mike Ambrose is the author of the question. Let the radius of the ascribed semicircle be 2 units. Therefore; Radius of the inscribed circle is 1 unit. It implies; Area R is; Area sector with radius 2 units and angle 45° - Area triangle with height and base √(2) unit each. = (45*2*2π÷360)-(½(√(2))² = ½(π)-1 = ½(π-2) square unit. Area S is; Area triangle with height and base √(2) unit each - Area sector with radius 1 unit and angle 90° + Area triangle with hei...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3024978

Let a be the side of the square. cos30 = b/8 b = 4√(3) cm. sin30 = c/8 c = 4 cm. a = b+12 a = (12+4√(3)) cm. Area Square is; a² = (12+4√(3))² = 358.27687752661 cm² d² = 12²+4²-2*4*12cos30 d = 8.76707255797 cm. (8.76707255797/sin30) = (12/sine) e = 180-43.18678543201 e = 136.81321456799° f = 360-e-180 f = 43.18678543201° g² = 8²+8.76707255797²+2*8*8.76707255797cos43.18678543201 g = 6.21165708246 cm. (6.21165708246/sin43.18678543201) = (8.76707255797/sinh)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3023335

Let the single side length of the two congruent inscribed regular pentagon be 1 unit. Area Green is; 0.5*5(1/(2tan(180/5))) = 1.72047740059 square units. Calculating Area Shaded. a = ⅕(180*3) = 108° Where a is the single interior angle of the congruent inscribed regular pentagon. b² = 2-2cos108 b = 1.61803398875 units. c = 1+b c = 2.61803398875 units. d² = 2.61803398875²+1²-2*1*2.61803398875cos72 d = 2.49721204096 units. Where d is the radius of the inscribed...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3021112

Sir Mike Ambrose is the author of the question. Area Orange exactly in square cm decimal is; Area triangle with height 1.64419338427 cm and base (4.95325421888sin129.5411167921) cm = ½*1.64419338427*(4.95325421888sin129.5411167921) = 3.14023734337 cm²

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