Mathematics Question and Solution
Calculating Shaded Area.
Notice.
The ascribed square side length is 1 unit.
tana = 1/½
a = atan(2)°
b = 2a
b = 2atan(2)°
c = b-90
c = 2atan(2)-90
c = 36.8698976458°
d = 180-b
d = 180-2atan(2)
d = 2atan(½)°
d = 53.1301023542°
e = ½(180-d)
e = 63.4349488229°
f = e-45
f = 18.4349488229°
g² = 2-2cos53.1301023542
g = 0.894427191 units.
h² = 2(½)²
h = 0.70710678119 units.
Area shaded gold is;
2(¼(π*1²)-½(1²))-2((53.1301023542π*1²÷360)-(0.5*1²sin53.1301023542)+(36.8698976458π*(0.5)²÷360)-(0.5*0.5²sin36.8698976458)+(0.5*0.894427191*0.70710678119sin18.4349488229))
= 2(0.7853981634-0.5)-2(0.463647609-0.4+0.0804376386-0.075+0.1)
2(0.2853981634)-2(0.1690852476)
= 0.5707963268-0.3381704952
= 0.2326258316 square units.
