Mathematics Question and Solution
Let the square side length be a.
Observing similar plane shape (right-angled) side length ratios.
8 - ½(a)
b - a
Cross Multiply.
½(ab) = 8a
b = 16 units.
c² = 8²+16²
c = √(64+256)
c = 8√(5) units.
d = ½(c)
d = 4√(5) units
d = 8.94427191 units.
d is the radius of the inscribed quarter circle and also the side length of the ascribed square.
d = a = 4√(5) units.
a = 8.94427191 units.
a is the height/length of the blue inscribed rectangle, the square side length, and also the radius of the inscribed quarter circle.
cose = (0.5/8)/4√(5)
e = acos(⅕√(5))°
cos(acos(⅕√(5))) = f/8
⅕√(5) = f/8
f = ⅕(8√(5)) units.
f = 3.577708764 units.
f is the width of the blue inscribed rectangle.
It implies;
Area Blue Inscribed Rectangle is;
fa
= ⅕(8√(5))*4√(5)
= ⅕*8*5*4
= 32 square units.
