Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3178622

Calculating Red Area. Let AB = CD = x. Let AD = BC = y. ½*xa = 10 a = 20/x units. a is BQ. ½*xb = 6 b = 12/x units. b is the horizontal height of area 6 (area triangle APB). c = y-b c = y-(12/x) c = (xy-12)/x units. c is the horizontal height of triangle CPD (red area). d = y-a d = y-(20/x) d = (xy-20)/x units. d is CQ. ½*e*(20/x) = 4 10e = 4x e = ⅖(x) units. e is the vertical height of area 4 (area triangle BPQ). Therefore; Calculating Area Rectangle ABCD (xy). ½*x*(xy-12)/x+½*(xy-2...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3177715

Calculating area ABCD. Let x be the radius of the inscribed circle. a = ½(16) a = 8 units. x² = 8²+a² a = √(x²-64) units. b = ½(25) units. It implies; x ~ 8 ½(25) ~ x Cross Multiply. x² = 100 x = 10 units. Again, x is the radius of the inscribed circle. c = 2x c = 20 units. c is the diameter of the inscribed circle, and also, the height of the isosceles trapezoid. sind = 10/(0.5*25) d = asin(20/25) d = asin(4/5)° tan(asin(4/5)) = 20/f f = 15 units. g = x-√(10²-(0.5*16)²) g = 10-√(1...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3177285

Calculating Area Yellow. ½*a²sin60 = 24 √(3)a² = 24*4 a² = 96/√(3) a = √(96/√(3)) a = 7.44483887282 units. a is the radius of the circle. b = a-x b = (7.44483887282-x) units. Calculating x. tan60 = (7.44483887282-x)/x √(3)x = (7.44483887282-x) (√(3)+1)x = 7.44483887282 x = 7.44483887282/(√(3)+1) x = 2.72500015453 units. cos30 = x/c c = 2.72500015453/cos30 c = 3.14655914552 units. d = a-c d = 7.44483887282-3.14655914552 d = 4.2982797273 units. It implies, ar...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3177282

Sir Mike Ambrose is the author of the question. Let the single side length of the square be 2 units. Area square is; 2² = 4 square units. Calculating green area. It will be; Area square of side 2 units - area triangle of two equal lengths ⅔(√(3)) units and angle 120°, the angle they form - area triangle of lengths (4-2√(3)) units and 2 units, and angle 60°, the angle they form. It implies; 4 - ½(⅔(√(3)))²sin120 - ½*2(4-2√(3))sin60 = 4 - ⅓√(3) - (2√(3)-3) = 4 - ⅓√(3) -2√(3) + 3 = 7 -...

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.

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