Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the square side be 1 unit.
Therefore;
Area B is;
Area triangle with height 1 unit and base sin(53.13010235416) unit - Area triangle with height 1 unit and base (0.71428571429sin(53.13010235416)) unit.
= ½*1(sin(53.13010235416)) - ½*1*(0.71428571429sin(53.13010235416))
= 0.4 - 0.28571428572
= 0.11428571428 square unit.
Area A is;
Area triangle with height 1 unit and base 0.5 unit + Area triangle with height 0.5√(5) unit and base sin10.30484646877 unit - Area sector with radius 1 unit and angle (10.30484646877+atan(0.5))°
= (½*1*½) + (½*0.5√(5)*sin10.30484646877) - ((10.30484646877+atan(0.5))*π÷360)
= ¼ + (1/10) - 0.3217505544
= 0.35 - 0.3217505544
= 0.0282494456 square unit.
It implies;
Area A ÷ Area B in decimal is;
0.0282494456 ÷ 0.11428571428
= 0.24718264901
= (706236140/2857129357) as a single fraction.
