Mathematics Question and Solution
Calculating Green Area.
Let x be the side length of the square.
a = ½(x) units.
a is the radius of the inscribed half circle.
tanb = ½(x)/x
b = atan(½)°
c = 2b
c = 2atan(½)°
d = 90-c
d = (90-2atan(½))°
d = 36.8698976458°
cos36.8698976458 = e/x
e = xcos36.8698976458 units.
Calculating x.
½*x*xcos36.8698976458sin36.8698976458 = 6
x²cos36.8698976458sin36.8698976458 = 12
0.48x² = 12
x = √(12/0.48)
x = 5 units.
Recall.
e = xcos36.8698976458
And x = 5 units.
e = 5cos36.8698976458
e = 4 units.
sin36.8698976458 = f/5
f = 3 units.
Therefore, area green is;
Area square with length 5 units - Area triangle with height 4 units and base 3 units.
= (5*5)-½(4*3)
= 25-6
= 19 square units.
