Mathematics Question and Solution
Notice.
7 square units is the are of the small pink half circle.
½*a²π = 7
And π = 22/7
½*a²(22/7) = 7
11a² = 49
√(11)a = 7
a = 7√(11)/11 units.
a = 2.110579412 units.
a is the radius of the small pink half circle.
b = 2a
b = 14√(11)/11 units.
b = 4.2211588241 units.
b is the diameter of the small pink half circle.
Let c be the side length of the small square.
Calculating c.
d = ⅛*180(8-2)
d = ⅛*180*6
d = ½*45*6
d = 135°
d is the single interior angle of a regular octagon.
e = ½(d)
e = 67.5°
It implies;
cos67.5 = c/4.2211588241
c = 1.6153675474 units.
Again, c is the side length of the small square.
sin67.5 = f/4.2211588241
f = 3.8998422411 units.
f is the side length of the big square.
g = c+f
g = 1.6153675474+3.8998422411
g = 5.5152097885 units.
h = f-c
h = 3.8998422411-1.6153675474
h = 2.2844746937 units.
Therefore;
j² = g²+h²
j² = 5.5152097885²+2.2844746937²
j = 5.969620058 units.
j is the diameter of the green half circle.
k = ½(j)
k = 2.984810029 units.
k is the radius of the green half circle.
Area green half circle is;
0.5πk²
= 0.5*π*2.984810029²
= 13.9943672753 square units.
≈ 14 square units.
