Mathematics Question and Solution
Notice;
The radius, a of the small inscribed circle is;
a = 2 units.
Calculating b, radius of the big circle.
c² = 8²+8²
c = √(128)
c = 8√(2) units.
d² = 2²+2²
d = √(8)
d = 2√(2) units.
It implies;
b = ½(c-d-a)
b = ½(8√(2)-2√(2)-2)
b = ½(6√(2)-2)
b = (3√(2)-1) units.
b = 3.2426406871 units.
2e² = (6√(2)-2)²
√(2)e = 6√(2)-2
e = ½(12-2√(2))
e = (6-√(2)) units.
f = 8-e
f = 8-(6-√(2))
f = (2+√(2)) units.
Area Green exactly is;
½(2+√(2))*6
= 3(2+√(2)) square units.
= 10.2426406871 square units.
Shaded Area exactly is;
¼(3√(2)-1)²π-½(3√(2)-1)²
= ¼(18-6√(2)+1)π-½(18-6√(2)+1)
= ¼(19-6√(2))π-½(19-6√(2))
=¼(19π-6√(2)π-38+12√(2)) square units.
= 3.0008813844 square units.
