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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3088475

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The radius of the circle with the inscribed square will be; ½(√(4²+4²)) = ½(√(32)) = ½(4√(2)) = 2√(2) cm. Therefore Blue Area will be; 2(area circle of radius 2cm) - area circle of radius 2√(2)cm + area square of single side length 4cm. It will be; 2(2²π) - ((2√(2))²π) +(4x4) = 8π - 8π + 16 = 16 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3086817

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Shaded/green area will be; Area semi circle of radius 9unit - 2(area sector of radius 9unit and angle 60°) + area equilateral triangle of single side length 9unit - area sector of radius 9unit and angle 50° - area quarter circle of radius 9unit + 2(area sector of radius 9unit and angle 60°) - area equilateral triangle of single side length 9unit = ½(81π) - ⅓(81π) + ¼(81√(3)) - ¼(45π) - ¼(81π) + ⅓(81π) - ¼(81√(3)) = ½(81π) - ¼(45π) - ¼(81π)  = ¼(162π - 45π - 81π) = ¼(162π - 126π...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3085580

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Notice; Single interior angle of a regular polygon with 6 sides (regular hexagon) is 120°. The formula to get it is; (180°(n-2))/n. Where n is the side number of the regular polygon. It implies; Blue area will be; Area regular hexagon with single interior angle and single side length 120° and 6cm respectively - 6(area sector of interior angle and radius 120° and 3cm respectively. = ¼((36x6)/tan(180/6)) - 6((120x9π)/360) = (54/tan30) - 18π = 54√(3) - 18π = 18(3...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3084164

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Let the radius of the bigger circle be 2 unit. Therefore the radius of the smaller circle will be; ½(2)=1 unit. Let the radius of the semi circle be r. It implies; 2² + r² = (1 + r)² 4 + r² = 1 +2r + r² 4-1=2r 2r=3 Therefore r (semi circle's radius) is; r=1.5 unit. Therefore; Area yellow circle : Area red semi circle is; (1)²π : ½(1.5)²π = 1 : ½(9/4) = 1 : (9/8) = 8 : 9 = 8/9

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3082980

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Blue area will be; Area square of single side length 4cm - 5(area circle of radius 1cm) + area square of single side 2cm. = 16 - 5π + 4 = 20 - 5π = 5(4 - π) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3081841

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Let x be a side length of the largest possible inscribed square of the scalene triangle with sides 13 cm, 14 cm and 15 cm respectively. It implies; x = 14÷((1/tan(53.13))+1+(1/tan(67.38))) x = 14÷(2.16667222427) x = 6.46152188743 cm. Therefore, area largest possible inscribed square A is; A = x² A = 6.46152188743² A = 41.7512651017 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3080388

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Calculating x (radius of the small inscribed circle) 28² + x² = (56-x)² 784 + x² = 3136 - 112x + x² 112x = 2351 x = 21 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3079025

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Calculating r, radius of the four congruent circles. Area square with side 2r cm - Area circle with radius r cm = Area green. (2r)² - πr² = 144π 4r² - πr² = 144π (4-π)r² = 144π r² = 144π/(4-π) r = √(144π/(4-π)) r = 12√(π/(4-π)) cm.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3077883

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Area Area Blue is; Area semi circle with radius √(2) units - Area quarter circle with radius 2 units + Area triangle with height and base 2 units respectively. = ½(√(2)²)π - ¼(2²)π + ½(2²) = π - π + 2 = 2 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3076680

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Area Blue is; Area triangle with height 4 cm and base (4sin150) cm = ½*4*(4sin150) = 2(4sin150) = 8sin150 = ½(8) = 4 cm²
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