Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Biggest square side is 14 units.
Bigger square side is 8 units.
a = atan(9/16)
(9/16) = b/c
c = (16b/9) units.
(16b/9)+6 = 14
(16b/9) = 8
b = (9/2) units.
c = (16*9/2)/9
c = 8 units.
d = 9-b
d = (9/2) units.
Where d is the side length of the big square.
Or
(9/16) = d/8
d = (9/2) units.
(e/sin(atan(9/16))) = (8/sin(180-atan(9/16)-atan(9/6))
e = 12√(13)/11 units.
f² = e²+(9/2)²-9ecos(90+atan(2/3))
f = 7.44025792675 units.
(7.44025792675/sin(90+atan(2/3)) = (3.93332866414/sing)
g = 26.09542415738°
h = 8-(9/2)
h = (7/2) units.
tan26.09542415738 = 2i/7
i = 1.71428571429 units.
j = 14-9-i
j = 3.28571428571 units.
It implies;
Area Red exactly in square units is;
(5*(9/2)) + (0.5*(7/2)(5+3.28571428571)) - (0.5*5*8)
= 22.5 + 14.5 - 20
= 37-20
= 17 square units.Biggest square side is 14 units.
Bigger square side is 8 units.
a = atan(9/16)
(9/16) = b/c
c = (16b/9) units.
(16b/9)+6 = 14
(16b/9) = 8
b = (9/2) units.
c = (16*9/2)/9
c = 8 units.
d = 9-b
d = (9/2) units.
Where d is the side length of the big square.
Or
(9/16) = d/8
d = (9/2) units.
(e/sin(atan(9/16))) = (8/sin(180-atan(9/16)-atan(9/6))
e = 12√(13)/11 units.
f² = e²+(9/2)²-9ecos(90+atan(2/3))
f = 7.44025792675 units.
(7.44025792675/sin(90+atan(2/3)) = (3.93332866414/sing)
g = 26.09542415738°
h = 8-(9/2)
h = (7/2) units.
tan26.09542415738 = 2i/7
i = 1.71428571429 units.
j = 14-9-i
j = 3.28571428571 units.
It implies;
Area Red exactly in square units is;
(5*(9/2)) + (0.5*(7/2)(5+3.28571428571)) - (0.5*5*8)
= 22.5 + 14.5 - 20
= 37-20
= 17 square units.
