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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3401084

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Calculating FM ÷ ML.Let 2 units be the side length of square.Calculating FM.tana = 2/1a = atan(2)°a is angle AFB.Let b, be the radius of the small inscribed circle.c = (1-b) units.Therefore;Calculating b.tan(½atan(2)) = b/(1-b)b = 0.6180339887(1-b)1.6180339887b = 0.6180339887b = 0.3819660112 units.Again, b is the small inscribed circle radius.It implies;c = 1-0.3819660112c = 0.6180339888 units.c is FM.Calculating ML.Let d, be the radius of the big inscribed circle.e = (2-d) units.Therefore;tan(...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3400047

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Calculating Blue Area.Let x be the radius of the inscribed white half circle.a = (1+x) cm.b = 1+1+xb = (2+x) cm.b is the radius of the ascribed half circle.Calculating x.x²+(1+x)² = (2+x)²x²+1+2x+x² = 4+4x+x²x² = 2x+3x²-2x-3 = 0x²-2x+(2/2)² = 3+(2/2)²(x-1)² = 4x = 1±√(4)x = 1±2It implies;x ≠ 1-2x = 1+2x = 3 cm.Again, x is the radius of the inscribed white half circle.Recall.b = 2+x, and x = 3 cm.b = 2+3b = 5 cm.Again, b is the radius of the ascribed half circle.Therefore, Area Blue is;½(π*5²)-½...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3398365

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Sir Mike Ambrose is the author of the question.Calculating Area R.Radius of the inscribed circle, r is;2r² = 4r² = 2r = √(2) units.Therefore;Area R in square unit to 3 d. p. is;Area sector with radius √(2) units and angle atan(0.5√(2))° - Area triangle with height 0.8165 units and base √(2)sin(atan(0.5√(2))) units - Area sector with radius 2 units and angle 25.5286945392° + Area triangle with height 2 units and base (2sin25.5286945392) units.= (atan(0.5√(2))π*√(2)²÷360) - (0.5*0.8165*√(2)sin(a...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3397210

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Sir Mike Ambrose is the author of the question.Calculating Area green exactly.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 unit 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-...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3396316

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Calculating Green Area.Area green is;Area square with side 6 units + 4(Area sector with radius 6 units and angle 60° - Area equilateral triangle with side 6 units) - Area square with diagonal (6√(3)-6) units - 4(area sector with radius 6 units and angle 30° - area triangle with height 6 units and base (6sin30) units).= 6² + 4((π6²)/6 - ¼(6²√(3))) - ½(6√(3)-6)² - 4((30π*36÷360)-½(36sin30))= 36 + 4(6π-9√(3)) - ½(144-72√(3)) - 4(3π-9)= 36 + 24π - 36√(3) - 72 + 36√(3) - 12π + 36= 24π - 12π= 12π sq...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3395146

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Sir Mike Ambrose is the author of the question.Calculating Area Triangle ABC ÷ Area Purple.Let the two equal side length of the ascribed isosceles triangle be 1 unit.Therefore;Area triangle ABC is;½(1*1sin36)= ½(sin36) space units.= 0.29389262615 square units.Area purple is;Area triangle with height 0.37567713613 units and base (0.15621533715sin138) units.= 0.5*0.37567713613*0.15621533715sin138= 0.01963447686 square units.It implies;Area Triangle ABC ÷ Area Purple to 2 d. p. is;0.29389262615...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3394143

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

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3394137

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Sir Mike Ambrose is the author of the question.Calculating 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/3393219

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Sir Mike Ambrose is the author of the question.Area orange exactly in cm² decimal form is;Area triangle with height 10 cm and base 4.28571428571 cm + Area triangle with height 8 cm and base (3.63654916039sin135) cm= (0.5*4.28571428571*10) + (0.5*8*3.63654916039sin135)= 21.4285714286 + 10.2857142857= 31.7142857143 cm²= 1174602/37037 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3393218

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Calculating x, the length that form tangents of the two semi circles.x²+2²=6²x²=36-4x²=32x = √(32) cm.x = 4√(2) cm.Therefore;Area blue is;Area trapezium with two parallel length 2 cm and 4 cm, and height 4√(2) cm - Area triangle with two length 4 cm each and angle atan(2√(2)) - Area triangle with two length 2 cm each and angle (90+ atan(1/(2√(2)))= ½(2+4)*4√(2) - ½(4²)sin(atan(2√(2))) - ½(2²)sin(90+ atan(1/(2√(2))))= 12√(2) - 7.54247233266 - 1.88561808316= 7.5424723326 cm²OrArea blue is;Area tr...
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