Mathematics Question and Solution
Let the square side be 2 units.
Area Square is;
2²
= 4 square units.
tana = ½
a = atan(½)°
b = 2a
b = 2atan(½)°
c = (180-2atan(½))°
d = atan(2)°
e = (180-2atan(½))-atan(2)
e = (90-atan(½))°
tan(0.5atan(2)) = f/1
f = 0.61803398875 units.
tan(0.5(90-atan(½))) = g/1
g = 0.61803398875 units.
Therefore;
Area Lilac is;
2*0.5(2*1)-4*0.5(1*0.61803398875 )
= 2-2*0.6180339887
= 0.7639320226 square units.
Area Lilac ÷ Area Square to 2 decimal places is;
0.7639320226÷4
= 0.19098300565
≈ 0.19
