Mathematics Question and Solution
Calculating the required red rectangle area.
a = √(4) = 2 units.
b = √(16) = 4 units.
c = √(9) = 3 units.
d = a+b
d = 2+4
d = 6 units.
e = b-a
e = 4-2
e = 2 units.
f² = 6²+2²
f = √(40)
f = 2√(10) units.
f is the length of the red rectangle.
g² = 3²+3²
g² = 18
g = √(18)
g = 3√(2) units.
g is the diagonal of the 9 square units, square.
h = 90-45-atan(2/6)
h = (45-atan(⅓))°
cos(45-atan(⅓)) = j/(3√(2))
j = 3√(2)cos(45-atan(⅓))
j = 3.7947331922 units.
j is the width of the red rectangle.
Therefore, area red rectangle is;
f * j
= 2√(10)*3.7947331922
= 24 square units.
