Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3176188

Let the single side length of the ascribed square be 2 units. Calculating yellow area . It is; Area sector with radius 2 units and angle (90-2tan–¹(½))°). = (90-2tan–¹(½))x4π÷360 = 1.28700221759 square units. Calculating red area. Area isosceles triangle with two equal lengths 1 unit each and angle (2tan–¹(2))°). =0.5sin(2tan–¹(2)) = 0.4 square units. Therefore; Area red ÷ Area yellow is; 0.4 ÷ 1.28700221759 = 0.31079977527

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3176178

Calculating Area Red. a = (1+x) units. a is the diameter of the circle. b = ½(a) b = ½(1+x) units. b is the radius of the circle. c = ½(1-x) units. Calculating x. (½(1+x))² = 2(½(1-x))² ¼(1+2x+x²) = 2*¼(1-2x+x²) 1+2x+x² = 2-4x+2x² x²-6x+1 = 0 (x-3)² = -1+(-3)² (x-3)² = 8 x = 3±2√(2) It implies; x ≠ 3+2√(2) units. x = 3-2√(2) units. x = 0.17157287525 units. Recall. b = ½(1+x) And a = 3-2√(2) units. b = ½(1+3-2√(2)) b = (2-√(2)) units. Again, b is the radius of the circle. d = 1-x d = 1-...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3175456

Calculating x. Let r be the radius of the inscribed green circle. Let R be the radius of the ascribed quarter circle. (R-r)² = r²+5² --- (1). (R-r)²+5² = a² --- (2). a² = x²+r² --- (3). Equating (3) and (2). (R-r)²+5² = x²+r² (R-r)² = x²+r²-5² --- (4). Equating (4) and (1). x²+r²-5² = r²+5² x²-5² = 5² x² = 5²+5² x² = 25+25 x² = 50 x = √(50) x = 5√(2) units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3175040

Calculating the area of the ascribed regular octagon. Let the equal longest length of the both inscribed yellow triangles be x. a = ⅛*180(8-2)) a = ⅛(180*6) a = ½(45*6) a = 135° a is the single interior angle of the ascribed regular octagon. sin(0.5*135) = (0.5x)/b b = 0.54119610015x units. b is the side length of the regular octagon. c = 135-(0.5*45)-½(360-2(135)) c = 135-22.5-45 c = 135-67.5 c = 67.5° c is the second bigger interior angle of inscribed triangle 21 square units. 2e² = (0....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3174823

Calculating Length AB. Let AB = (a+7+b) units. Calculating a and b. c = (7+b) units. Therefore; a(7+b) = 60 a = 60/(7+b) --- (1). Again. d = (a+7) units. Therefore; b(a+7) = 5*12 ab+7b = 60 ab = 60-7b a = (60-7b)/b --- (2). Equating (1) and (2) to get b. 60/(7+b) = (60-7b)/b Cross Multiply. 60b = 420-49b+60b-7b² 7b²+49b-420 = 0 b²+7b-60 = 0 b²+12b-5b-60 = 0 b(b+12)-5(b+12) = 0 (b+12)(b-5) = 0 Therefore; b ≠ -12 b = 5 units. Calculating a, us...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3174819

Shaded Area is; Area circle with radius 4 cm - 4(area quarter circle with radius 4 cm - area isosceles right-angled triangle with equal adjacent lengths 4 cm). = π*4²-4(¼(4²π)-½(4²)) = 16π-4(4π-8) = 16π-16π+32 = 32 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3174279

Calculating Red Area. A nice and careful examination of the irregular pentagon, makes a regular quadrilateral (square) with side length 1 cm. It implies; Red area is; 1² = 1*1 = 1 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3173559

Calculating Yellow Area. Let a be the side length of the square. b = ½(a) units. c² = a²+(½(a))² c² = ¼(5a²) c = ½√(5)a units. c is the radius of the half circle. It implies; a ~ ½√(5)a d ~ a Cross Multiply. ½√(5)d = a d = 2a/√(5) d = ⅕(2√(5)a) units. e = ½(d) e = ⅕√(5)a units. f = c-e f = ½√(5)a-⅕√(5)a f = ⅒(3√(5))a units. Calculating a. ½*a*½(a)+½*⅒(3√(5))a*⅕(2√(5)a) = 15 ¼(a²)+⅒(3a²) = 15 5a²+6a² = 300 11a² = 300 a = 10√(3)/√(11) a = 10√(33)/11 units. g = 2f g = 2*⅒(3√(5))a g = ⅕(...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3173553

Calculating Yellow Area. a = ½(24) a = 12 units. b² = 12²+c² c = √(b²-144) units. Where; b is the ascribed half circle's radius. c is the inscribed half circle's radius. Area yellow is; ½(πb²)-½(πc²) = ½(πb²)-½(π√(b²-144)²) = ½(πb²)-½(πb²)+½(144π) = 72π square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3173552

Calculating R, radius of the circle. Notice. 3 units is the side length of the inscribed yellow square. 2 units is the side length of the inscribed red square. 1 unit is the side length of the inscribed blue square. And; Length BT = Length BC. Therefore; a² = 2(3)² a = 3√(2) units. a is BC. b² = 2(1.5)² b = 1.5√(2) units. b is OB. It implies: R² = a²+b² R² = (3√(2))²+(1.5√(2))² R² =18+4.5 R = √(22.5) R = ½(3√(10)) units. R = 4.74341649025 units.

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