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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

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3075350

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Shaded Area is; Area circle with diameter 30 cm - 7(area circle with diameter 10 cm) = π(½(30))² - 7π(½(10))² = π(15)² - 7π(5)² = 225π - 175π = 50π cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3074102

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Sir Mike Ambrose is the author of the question. Let CD = 2 units. Therefore; Calculating AB. AB = 1 + (2sin18*tan72 + 2sin36)tan54 AB = 1 + 3.07768353717tan54 AB = 1 + 4.23606797749 AB = 5.23606797749 units. It implies; Length AB ÷ Length CD to 2 decimal places is;  5.23606797749 ÷ 2 = 2.61803398874  ≈ 2.62

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3072681

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x² = (r+1)² - (r-1)² Therefore x = 2√(r) unit. y² = (r+1)² - (2√(r))² Therefore y = √(r²-2r+1) y = √(r-1)² y = (r-1) unit z = (r+1) - y z = (r+1) - (r-1) Therefore z = 2 units a = r+r Therefore a = 2r units A sincere study and analysis of the composite circles deduced a right-angled triangle with two adjacent sides, 2 units and 2√(r) units respectively, and hypotenuse 2r units. Therefore; Calculating r, the radius of the three congruent circles. (2r)² = 2² + (2√(r)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3071591

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Area R is; Area sector with radius 8 cm and angle 20.16632290743° - Area triangle with height 8 cm and base (4.2sin 20.16632290743) cm = ( 20.16632290743 *64π÷360) - (½*8*4.2sin 20.16632290743) = 11.26299944816 - 5.79174146157  = 5.47125798659 cm² ≈ 5.47 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3070480

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Area coloured is; Area sector with radius 3 units and angle 120° - Area triangle with height 3 units and base 3sin120 units + Area triangle with height 3 units and base 3sin60 = (120*9π÷360) - (½*9*½*√(3)) + (½*9*½√(3)) = 3π - ¼(9√(3)) + ¼(9√(3)) = 3π square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3069482

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Shaded area is; Area sector with radius 10 cm and angle 60° (100π*60)/360 = (100π)/6 = ⅓(50π) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3068717

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Let the side length of the regular heptagon be 1 unit. a = ⅐(180*5) a = ⅐(900)° b = 0.5(360-2(900/7)) b = ⅐(360)° c = 2cos(360/7)+1 c = 2.24697960372 units. d² = 2-2cos(90/7) d = 1.8019377358 units. Where d is the radius of the arc. Area Orange is; 0.5*2.24697960372*1sin(360/7)+0.5*sin(900/7) = 1.26929543856 square units. Let e be alpha. Calculating e. e = 0.5((900/7)-(360/7)) e = ⅐(270)° (1.8019377358/sin(270/7)) = (2.24697960372/sinf) f = 128.96966294...
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