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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3545599

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Exact enclosed area R.It is;Area sector with radius 2 units and angle (90-2tan–¹(½)) - Area sector with radius 1 unit and angle (180-4tan–¹(½)) + Area isosceles triangle with two equal lengths 1 unit and angle (180-4tan–¹(½)).=((90-2tan–¹(½))x4π÷360) - ((180-4tan–¹(½))xπ÷360) + 0.5sin(180-4tan–¹(½))= 1.1235011088 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3544731

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Calculating Green Area : Red Area.Let x be the red square side length.Let 2 units be the green square red length.Area green is;2²= 4 square units.Calculating x.a = (2-x) units.b = 90-60b = 30°tan30 = c/xc = x/√(3)c = ⅓(√(3)x) units.d = x-cd = x-⅓(√(3)x)d = ⅓(3-√(3))x units.It implies;x ~ ⅓(3-√(3))x2 ~ (2-x)Cross Multiply.⅔(3-√(3)) = 2-x6-2√(3) = 6-3x3x = 2√(3)x = ⅔√(3) units.Again, x is the side length of the red square.Area red square is;x²= (⅔√(3))²= 4/3 square units.Therefore, Green Area : R...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3543645

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Calculating Angle x.Let 2 units be the radius of the ascribed quarter circle and a be the radius of the inscribed circle.Calculating a.b = (2-a) units.It implies;2a² = (2-a)²2a² = 4-4a+a²a²+4a-4 = 0(a+2)² = 8a = -2±√(8)It implies;a = (2√(2)-2) units.a = 0.82842712475 units.Again, a is the radius of the inscribed circle.tanc = 2/0.82842712475c = 67.4999999999c = 67.5°d = 90-cd = 90-67.5d = 22.5°Therefore, the required angle, x is;x = d+45x = 22.5+45x = 67.5°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3543012

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Calculating Length EF.Let x be EC = CH, radius of the small inscribed circle.a = (20-x) cm.tanb = 10/20b = atan(½)°c = ½(90-2atan(½))c = ½(atan(2)-atan(½))c = 18.4349488229°Calculating x, radius of the small inscribed circle.tan18.4349488229 = x/(20-x)20tan18.4349488229-xtan18.4349488229 = xx+xtan18.4349488229 = 20tan18.4349488229x = (20tan18.4349488229)÷(1+tan18.4349488229)x = 5 cm.d² = 5²+20²d = 5√(17) cm.d = 20.6155281281 cm.tane = 5/20e = atan(¼)°f = 90-2atan(½)-atan(¼)f = 22.8336541779°It...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3542010

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Calculating Area Green Inscribed Square.Let x be the side length of the green square.a² =2x²a = √(2)x units.a is the radius of the ascribed half circle.b² = (√(2)x)²+x²b² = 2x²+x²b = √(3)x units.c = 2+bc = (2+√(3)x) units.Calculating x.It implies;(2+√(3)x) ~ √(2)x2√(2)x ~ √(3)xCross Multiply.4x² = 2√(3)x+3x²x² = 2√(3)xx = 2√(3) units.Again, x is the side length of the inscribed green square.Therefore, area inscribed green square is;x²= (2√(3))²= 12 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3541334

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Calculating radius of the largest half circle and area yellow.a = 2+3a = 5 units.b²+3² = 5²b = √(16)b = 4 units.c = 2+b+3c = 2+4+3c = 9 units.Where c is the length or base of the rectangle.d = ½(c)d = 4.5 units.Calculating r, radius of the largest half circle.4.5²+3² = r²r = = √(29.25)r = ½(3√(13)) units.r = 5.4083269132 units.Calculating Area Yellow.tane = 3/4.5e = atan(3/4.5)e = 33.690067526°f = 180-ef = 146.309932474°Area Yellow is;Area rectangle with length 9 units and width 5.4083269132 un...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3540199

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Calculating Area Green.Notice.The opposite angles are congruent.Let them be x each.a = (360-x)°Calculating x.½(a) = x½(360-x) = x360-x = 2x3x = 360x = 120°b² = 9²+6²-2*9*6cos120b = 3√(19) units b = 13.0766968306 units.c = ½(b)c = ½(13.0766968306)c = 6.53834841531 units.Calculating r, radius of the green sector.sin(0.5*120) = 6.53834841531/r½√(3) = 6.53834841531/r√(3)r = 2*6.53834841531r = √(57) units.r = 7.54983443527 units Therefore, area green sector is;120*π√(57)²÷360= ⅓(57π)= 19π square uni...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3539524

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Notice.Three Congruent Half Circles With Area 72 cm² Each.Calculating Area Blue.Calculating r, Radius of the half circle.½(22/7)r² = 72Where π = 22/7(11/7)r² = 7211r² = 504r = √(504/11)r = 6.76891289781 cm.a = 2(60π*6.76891289781²/360)-(½(6.76891289781)²sin60)a = 28.1408330954 cm²b = 60-20b = 40°c = (40π*6.76891289781²÷360)+(60π*6.76891289781²÷360)-(0.5*6.76891289781²sin60)c = 20.1440517953 cm²It implies;Area Blue is;a-c= 28.1408330954-20.1440517953= 7.9967813001= 8 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3538594

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Calculating Area Blue.Blue area is;Area circle of radius 3cm - 2(area circle of radius 1cm) + area rectangle with length 6cm and width 4cm - 2(area square with single side length 1cm) - area circle of radius 1cm - 2(quarter circle of radius 2cm.= 3²π - 2(1²π) + (6x4) - 2(1x1) - (1²π) - 2(¼(2²π))= 9π -2π + 24 - 2 - π - 2π= 9π - 5π + 24 - 2= 4π + 22= 2(2π+11) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3537519

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Calculating Angle x.Let the single side length of the regular pentagon be 4 units.Therefore angle x degree will be;sinx = (2/4)sinx = ½Therefore;x = sin–¹(½)x = 30°
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