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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2619978

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Sir Mike Ambrose is the author of the question. Area D exactly in cm² is; Area trapezoid with parallel sides 4 cm and 8 cm, and height 4 cm - Area triangle with height 4 cm and base 3 cm - Area sector with radius 4 cm and angle atan(4/3). = (½*4(4+8)) - (½*4*3) - (atan(4/3)*π*4²÷360) = 24 - 6 - (2πatan(4/3))/45 = 18 - (2πatan(4/3))/45 = (810 - (2πatan(4/3)))/45 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2619972

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Yellow area will be; ½(12) - (½(⅔√(3))²xsin(atan(3))÷sin(135-atan(3)))xsin(45) = 6 - (½) = ½(12-1) = ½(11) = 5.5 square unit.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2619965

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Area red is; ½(3*4) - (atan(4/3)x9π÷ 360) - (atan(3/4)x4π÷ 360) = 0.54016930141 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2618498

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Calculating Angle x. Let the two equal lengths of the ascribed triangle be 1 unit each. a = 180-40-30 a = 110° b = 180-a b = 70° (1/sin40) = (c/sin30) c = 0.7778619134 units. Therefore, the required angle, x is; (0.7778619134/sinx) = (1/sin70) x = 46.9661874908°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2618483

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Radius of the ascribed quarter circle is; 1+1 = 2 cm. a² = 1²+2² a = √(5) cm. Observing similar plane shape (right-angled) side length ratios. √(5) - 4 1 - b Cross Multiply. b = ⅕(4√(5)) cm. c²+b² = a² c² = √(5)²-(⅕(4√(5)))² c² = 5-(80/25) c = ⅕√(45) cm. Therefore, area inscribed green quadrilateral is; Area triangle with height 1 cm and base 2 cm + Area triangle with height ⅕(4√(5)) cm and base ⅕√(45) cm. (½*1*2)+(½*⅕√(45)*⅕(4√(5))) = 1+ ⅕(6) = 2⅕ cm² =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2618457

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

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2618448

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Let the radius of the semicircle be r. Therefore; r²= (1+√(3))²+(½)² r²=1+2√(3)+3+¼ r²=4+¼+2√(3) r²=¼(17+8√(3) r = ½√(17+8√(3)) units. r = 2.77742715749 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2618441

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Let the radius of the circle be r. Therefore; (2r)²=2(√(20))² 4r²=40 r = √(10) unit. Therefore area of the circle is; πr² π(√(10))² = 10π square unit.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2616946

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Sir Mike Ambrose is the author of the question. Area Orange in cm² to 2 decimal places is; Area triangle with height 4.70800619717 cm and base (4.09924763539sin35.93797861993) cm + Area triangle with height 4.70800619717 cm and base (4.18128805798sin17.19212373423) cm = ½*4.70800619717*(4.09924763539sin35.93797861993) + ½*4.70800619717*(4.18128805798sin17.19212373423) = 5.66346312039 + 2.9092922885 = 8.57275540889 cm² ≈ 8.57 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2615404

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Notice! The composite plane shape consist of two squares. Calculating length x. Sin30 = 1/a a = 2 units. a is the side length of the bigger square. b² = 2a² b² = 2(2²) b = √(8) b = 2√(2) units. b is the diagonal of the bigger square. c = 45-30 c = 15° Therefore, the required angle, x is; x² = 1+(2√(2))²-2*1*2√(2)cos15 x = √(9-4√(2)cos15) x = √(9-2(1+√(3)) x = √(7-2√(3)) units. x = 1.8803984644 units.
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