Mathematics Question and Solution
Calculating Red Area.
Notice.
45 cm is the side length of the square.
a = 45-9-18
a = 18 cm.
tanb = 45/18
b = atan(5/2)°
c = 180-b
c = 180-atan(5/2)
c = (90+atan(2/5))°
c = 111.801409486°
d = ½(90)
d = 45°
e = 180-c-d
e = 180-111.801409486-45
e = 23.198590514°
It implies;
(18/sin23.198590514) = (f/sin111.801409486)
f = 42.4264068707 cm.
g² = 2(45)²
g = 45√(2) cm.
g = 63.6396103068 cm.
g is the diagonal of the square.
h = g-e
h = 63.6396103068-42.4264068707
h = 21.2132034361 cm.
It implies the red area is;
2(½*18*42.4264068707sin45)+2(½*9*21.2132034361sin45)
= (18*42.4264068707sin45)+(9*21.2132034361sin45)
= 539.999999994+135.000000003
= 675 cm²
