Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the square side be 2 units.
Area Square is;
2²
= 4 square units.
Calculating Area Yellow.
(2-a)²+1 = a²+4
4-4a+a²+1=a²+4
a = ¼ unit.
b² = 1+(65/64)-2*⅛(√(65))cos(atan2+atan(3/2))
b = ⅛√(193) units.
(b/sin(atan2+atan(3/2))) = ((⅛√(65))/sinc)
c = asin(7√(193)/193)°
c = 30.25643716353°
d = acos(7√(193)/193)°
d = 59.74356283647°
e² = 4+(193/64)-(2*2√(193)/8)cos(acos(7√(193)/193))
e = (15/8) units.
(15/8sin(acos(7/√(193)))) = (√(193)/8sinf)
f = asin(4/5)°
g = (asin(4/5)-atan(½))°
g = 26.56505117708 °
h = ½(√(5)tan(asin(12/15)-atan (½)))
h = ¼√(5) units.
i = √(5)- (7√(5)/31)
i = (24√(5)/31) units.
Area Yellow is;
Area triangle with height ⅛√(193) units and base 2sin(acos(7/√(193))) units - Area triangle with height (24√(5)/31) units and base 2sin(atan(1/2)) units - Area triangle with height ½√(5) units and base ¼√(5) units.
= ½*⅛√(193)*2sin(acos(7/√(193))) - ½*(24√(5)/31)*2sin(atan(1/2)) - ½*½√(5)*¼√(5)
= ½(3) - (24/31) - (5/16)
= 205/496 square units.
It implies;
Area Yellow ÷ Area Square exactly is;
(205/496) ÷ 4
= 205/1984
