Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2843870

Sir Mike Ambrose is the author of the question. Let the side length of the three congruent, inscribed square be x. Calculating x. x + 2 = 2√(3) x = (2√(3)-2) units. Therefore; Area green exactly in square units decimal form is; Area triangle with height (2√(3)-2) units and base (4-2√(3)) units + Area triangle with height (2√(3)-2) units and base ⅓(6-2√(3)) units + Area triangle with height 1.55909609016 units and base ⅓(4√(3)-6)sin(50.103909361) units. = (0.5*(2√(3)-2)(4-2...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2843843

Let a be the side of the square. cos30 = b/8 b = 4√(3) cm. sin30 = c/8 c = 4 cm. a = b+12 a = (12+4√(3)) cm. Area Square is; a² = (12+4√(3))² a² = 358.27687752661 cm² d² = 12²+4²-2*4*12cos30 d = 8.76707255797 cm. (8.76707255797/sin30) = (12/sine) e = 180-43.18678543201 e = 136.81321456799° f = 360-e-180 f = 43.18678543201° g² = 8²+8.76707255797²+2*8*8.76707255797cos43.18678543201 g = 6.21165708246 cm. (6.21165708246/sin43.18678543201) = (8.76707255797/s...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2842333

Let the diameter of the inscribed white semicircle be x. Therefore the diameter of the ascribed semicircle is 2x. Calculating x. (3x/2)² = x²+36 (9x²/4)-x² = 36 (5x²/4) = 36 √(5)x = 12 x = ⅕(12√(5)) units. Where x is the radius of the ascribed semicircle. Radius of the inscribed white semicircle is; ½(x) = ⅕(6√(5)) units. Area Blue is; π½(⅕(12√(5)))² - π½(⅕(6√(5)))² = ½(π(⅕(108))) = ⅕(54π) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2842327

Sir Mike Ambrose is the author of the question. Area purple is; Area trapezoid with two parallel sides 4 cm and (50/9) cm, and height (7/2) cm - Area triangle with height 4 cm and base 3 cm. = ½(4+(50/9))*(7/2) - ½(4*3) = (602/36) - 6 = 193/18 cm² Area orange is; Area trapezoid with two parallel sides 6 cm and (40/9) cm, and height (7/2) cm - Area triangle with height (40/9) cm and base (40/13) cm. = ½(6+(40/9))*(7/2) - ½((40/9)*(40/13)) = (329/18) - (800/117) = 4277/234...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2840749

Let the height of the yellow area trapezoid be a. Calculating a. tan72 = a/b b = (a/tan72) cm. c = 2b c = (2a/tan72) cm. d = 8+c d = (8+(2a/tan72)) cm. It implies; ½*a(8+(8+(2a/tan72))) = 56.23 a(16+0.64983939247a) = 112.46 0.64983939247a²+16a- 112.46 = 0 Therefore; a = 5.70627 cm. d = (8+(2a/tan72)) d = 11.70815903005 cm. tan18 = e/5.70627 e = 1.85407951502 cm. f = 2e f = 3.70815903005 cm. (g/sin36) = (8/sin108) g = 4.94427191 cm. sin72 = h/8...

Mathematics Question and Solution.

https://onlineedumath.com/update/mathematics-question-and-solution/2840743

Sir Mike Ambrose is the author of the question. Let AB be 2 unit. Therefore CD = 1 unit. It implies; Area Blue is; Area triangle with height 0.72111025509 unit and base sin(atan(3/2)) unit. = 0.5*0.72111025509sin(atan(3/2)) = 3/10 space unit. Area Green is; Area trapezoid with two parallel side (3/2) unit and 1 unit, and height ½ unit - Area triangle with height (3/2) unit and base ½ unit. = ½*½((3/2)+1) - ½*½(3/2) = (5/8) - (3/8) = ¼ space unit. Area Red is; Area...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2839130

Sir Mike Ambrose is the author of the question. Area brown exactly in square unit decimal is; Area brown exactly in square unit decimal is; Area triangle with height 2 unit and base (1.93220910506sin(120-atan(2√(3))) unit. = (1.93220910506sin(120-atan(2√(3)))) cm² = 1.39230484541 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2839118

Let the square side be x. x²+(x-4)² = a² a = √(2x²-8x+16) b² = 2²+(x-2)² b = √(x²-4x+8) It implies; (½(a))²+6² = b² ½(x²-4x+8)+36 = (x²-4x+8) x²-4x+8+72 = 2x²-8x+16 x²-4x-64 = 0 (x-2)² = 68 x = 2±2√(17) x = 2+2√(17) units. Area Shaded is; ½(x)² = ½(2+2√(17))² = 4(9+√(17)) square units. = 52.49242250247 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2837758

Hexagon Area = 1 square units. Calculating the regular hexagon side length. Let it be a. (6a²)/(4tan30) = 1 3a² = 2/√(3) a² = ⅑(2√(3)) a = ⅓(√(2√(3))) unit. a = 0.6204032394 units. (b/sin30) = (0.6204032394/sin120) b = 0.35818997727 unit. Shaded region area is; 2(0.5*0.6204032394²sin120) - (0.5*0.35818997727*0.6204032394sin30) = ⅓ - (1/18) = (6-1)/18 = 5/18 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2837750

Area blue is; Quarter the area of the square. = ¼(10)² = ¼(100) = 25 cm²

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