Mathematics Question and Solution
Let the radius of the inscribed half circle be 1 unit.
Area rectangle is;
2*1
= 2 square units.
Calculating Shaded Area as a single fraction..
It is;
½(1*2) - 1² + ¼(1)²π - ((180-2atan(½))π*1²/360) + (0.5*1²sin(180-2atan(½)))
= 1-1+¼(π)-(π(180-2atan(½))/360)+⅖
= (π/4)+⅖-(π(180-2atan(½))/360)
= ((5π+8)/20)-(π(180-2atan(½))/360)
= (90π+144-180π+2πatan(½))/360
= (144-90π+2πatan(½))/360 square units.
Therefore;
Area Shaded ÷ Area Rectangle as a single fraction is;
((144-90π+2πatan(½))/360) ÷ 2
= (144-90π+2πatan(½))/720 square units.
