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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2562836

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Radius of the inscribed quarter circle is 36 cm. Radius of the inscribed semi circle is; ½(½(36))=9 cm. Radius of the small inscribed circle is; ⅓(⅓(36))=4 cm. Therefore the side lengths of triangle blue will be; (36+9)=45 cm. (36+4)=40 cm. (9+4)=13 cm. Therefore area triangle blue is; 0.5x45x40sin(cos–¹((45²+40²-13²)÷(2x45x40))) = 252 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2562365

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Notice! The square side length is; 4+4+4 = 12 units. Calculating Area Red. 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 respectively. = ¼(π*12²...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2558688

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Shaded area will be; Area semi circle of radius √(2) cm - area quarter circle of radius 2 cm + area square of single side length √(2) cm. = ½(√(2))²π - ¼(2²)π + (√(2))² = π-π+2  = 2 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2558651

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Shaded area will be; Area quarter circle of radius 2 unit + 2(area quarter circle of radius √(2) unit - area triangle of height and base √(2) unit respectively). = ¼(4π) + 2(¼(2π) - ½(2)) = π + π - 2 = 2(π-1) square units. Or a² = 2(2)² a = √(8) a = 2√(2) units. b = ½(a) b = √(2) units  Shaded Area is; Area semi circle with radius √(2) units - Area isosceles right-angled triangle with adjacent sides 2 units each + Area quarter circle with radius 2 units. (½*π*√(2)²)-...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2557528

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Let the single side length of the ascribed square be 2 unit. Therefore area of the ascribed square is; 4 square unit. Calculating shaded area (area yellow). It will be; Area square of single side length 2 unit - area circle of radius 1 unit + 8(area quarter of radius ½√(2) unit - area triangle of height and base ½√(2) unit respectively). = 4 - π + 8(¼(½√(2))²π - ½(½√(2))² = 4 - π + 8(⅛(π) - ¼) = 4 - π + π - 2 = 2 square unit. Therefore shaded fraction is; Area yellow (shaded area) ÷ Ar...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2556760

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Notice! AC = 7+7 AC = 14 units. It implies; 14² = 2a² a² = ½(196) a = √(98) a = 7√(2) units. a is the side length of square ABCD. Therefore, shaded area yellow is; Area square with side length 7√(2) units - 2(area quarter circle with radius 7 units). = (7√(2)*7√(2))-2(¼*7*7π) For π = (22/7) = 98-½(22*7) = 98-77 = 21 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2555779

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a² = 3²+4² a = √(25) a = 5 cm. a is the radius of the quarter circle. Let r be the radius of the inscribed blue circle. Calculating r. b = (3+r) cm. c = (5-r) cm. It implies; (5-r)² = (3+r)²+r² 25-10r+r² = 9+6r+r²+r² r²+16r-16 = 0 Resolving the above quadratic equation via completing the square approach to get r, radius of the inscribed blue circle. (r+8)² = 16+(8)² (r+8)² = 80 r = -8±√(80) r = -8±4√(5) It implies; r = (4√(5)-8) cm. r = 0.94427191 cm....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2555576

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Area red is; Area semi circle with radius 5 cm - Area sector with radius 5 cm and angle (180-2atan(2))° - Area kite with diagonal lengths √(10²+5²) cm and √(200-200cos(2atan(½))) cm + Area sector with radius 10 cm and angle 2atan(½)° - 2(area quarter circle with radius 5 cm - area triangle with height and base 5 cm respectively). = 12.5π - 11.591190225 - 50 + 46.3647608999 - 14.2699081699 = 9.77357067487 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2554627

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Notice! BD is the diameter of the circle. a = ½(BD)  a = ½(14) a = 7 cm. a is OB = OD. a is the radius of the circle. b = 2(45) b = 90° b is angle AOB. Calculating shaded area. It is; Area quarter circle with radius 7 cm - Area triangle with height and base 7 cm respectively. = ¼(7*7)π-½(7*7) = ¼(49π)-½(49) = ¼(49π-98) = ¼(49(π-2)) square units. = 13.9845100065 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2554553

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Notice! The radius of the quarter circle is 4 units. 4² = 2²+a² 16-4 = a² a = √(12) a = 2√(3) units. It implies, area green is; Area triangle with height 2√(3) units and base 2 units. = ½*2√(3)*2 = 2√(3) square units.
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