Mathematics Question and Solution
Let the radius of the ascribed quarter circle be 2 units.
Radius inscribed semi circle is 1 unit.
Therefore;
Area Semi Circle is;
½(π) square units.
Calculate Area Shaded.
tana = ½
a = atan(½)°
b = 2a
b = 2atan(½)°
c = (180-4atan(½))°
d² = 2²+2²-2*2*2cos(180-4atan(½))
d = 2.4 units.
e = 2.4-2
e =0.4
e = 2/5 units.
tanf = (2/5)/1
f = atan(2/5)°
Shaded Area is;
½*⅖*1 - (πatan(2/5)/360)
= ⅕-(πatan(2/5)/360)
= (72-πatan(2/5))/360 square units.
Therefore;
Area Shaded ÷ Area Semi Circle as a single fraction is;
((72-πatan(2/5))/360)÷(π/2)
= (72-πatan(2/5))/180π
= 0.0062050129 exactly in decimal.
