Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2956599

Let the radius of the inscribed circle be r. The square side is 8 cm. b = 8-r c = 2+r Therefore; (2+r)² = 2²+(8-r)² 4+4r+r² = 4+64-16r+r² 4r = 64-16r 20r = 64 5r = 16 r = (16/5) cm. Area circle is; πr² = 256π/25 cm² = 32.16990877276 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2954769

Sir Mike Ambrose is the author of the question. Let length AB = 2 units. Therefore; Side length of the square, x is; 2x² = 2² x = √(2) units. It implies; Area square is; x² = √(2)² = 2 square units. Area green is; Area triangle with height √(3) units and base 1 unit - Area triangle with height ⅓√(3) units and base 1 unit - Area triangle with height tan15 units and base 1 unit. = ½(√(3)*1) - ½(⅓√(3)*1) - ½(tan15*1) = ½√(3) - (√(3)/6) - ½(tan15) = ⅓√(3...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2953008

Sir Mike Ambrose is the author of the question. Inscribed square single side length is; 7.80540954246 cm Area green in cm² to 1 decimal place is; Area trapezoid with parallel sides 12 cm and 7.25948291225 cm, and height 12 cm - Area square with side 7.80540954246 cm - Area triangle with height 7.25948291225 cm and base 2.86780856615 cm. = ½*12(12+7.25948291225) - 7.80540954246² - ½*7.25948291225*2.86780856615 = 115.556897474 - 60.9244181255 - 10.4094036408 = 44.2230757077 c...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2951172

Sir Mike Ambrose is the author of the question. Let the side let of the square be 2 units. Therefore; Area square is; 2² = 4 square units. It implies; Area R is; Area trapezoid with parallel sides 1 unit and 1.44948974279 unit, and height 2 unit - Area square with side 1 unit - Area triangle with base and height 1 unit respectively - Area sector with radius √(2) unit and angle 32.3335306935° - Area triangle with height √(2) unit and base 0.3178372452 unit = (½*2(1+1.4...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2949480

Area blue is; Area triangle with height 10 cm and base (10sin16.26025509) cm - Area semi circle with radius √(2) cm = (0.5*10*10sin16.26025509) - (½π√(2)²) = (14-π) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2949443

Let AB = x PB = x/4 Therefore; a = x - (x/4) a = (3x/4) units. b² = x²+(3x/4)² b = √(x²+(3x/4)²) units. c = (x-4) units. It implies that; ½(x*(3x/4)) + ½(4*√(x²+(3x/4)²)) + ½(4*(x-4)) + (4*4) + ½((x/4)+4)*(x-4) = x² ⅛(3x²) + 2√(x²+(3x/4)²) + 2(x-4) + 16 + ½(¼(x+16))(x-4) = x² 2√(x²+(3x/4)²) + 2x + 8 + ⅛(x²+12x-64) = ⅛(5x²) 16√(x²+(3x/4)²)+16x+64+x²+12x-64 = 5x² 16√(x²+(3x/4)²)+28x = 4x² Dividing through by 4 4√(x²+(3x/4)²)+7x = x² 16(x²+(9x²/16)) = x⁴...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2947966

Sir Mike Ambrose is the author of the question. Let the single side length of the square be 2 unit. Therefore; Area square is; 2² = 4 square units It implies; Area R is; Area sector with radius 2 unit and angle 8.130127545° - Area triangle with height 1.61624318301 unit and base (1.37930921037sin8.130127545) unit = (8.130127545*4π÷360) - (½*1.61624318301*1.37930921037sin8.130127545) = 0.28379498853 - 0.15763573684 = 0.12615925169 square unit Therefore; Ar...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2946129

Red Area is; 7(area square with side 1 unit) - Area triangle with base 1 unit and height 4 units - Area square with side 1 unit - Area triangle with height and base 1 unit respectively. = 7(1*1) - 0.5(1*4) - (1*1) - 0.5(1*1) = 7 - 2 - 1 - 0.5 = 3.5 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2945011

The radius of the inscribed circle is 2 units. a = 2atan(⅓)° b = 2atan(⅕)° c = 180-a-b c = (180-2atan(⅓)-2atan(⅕))° sin(2atan(⅓)) = d/16 d = (48/5) units. cos(2atan(⅓)) = e/16 e = (64/5) units. f = (90-2atan(⅓)-2atan(⅕))° tan(90-2atan(⅓)-2atan(⅕)) = g/(48/5) g = (198/35) units. Therefore; Area Blue exactly in square units is; ½*(48/5)(198/35) = 4752/175 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2943951

8 = 4 a = (8-a) Cross multiply. 64-8a = 4a 64 = 12a a = ⅓(16) cm. b = 8-a b = ⅓(8) cm. c = atan(⅔)° d = atan(3/2)° ⅔ = 8/e e = 12 cm ⅔ = f/8 f = ⅓(16) cm. g = 8-f g = ⅓(8) cm. Area Orange exactly in cm² is; Area square units side 8 cm - Area rectangle with length 4 cm and width ⅓(8) cm. = 8² - 4*⅓(8) = 64 - ⅓(32) = ⅓(192-32) = ⅓(160) cm²

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