Let x be the single side length of the square.
Therefore;
x²=28-4√(x²-16) via similar triangle.
16(x²-16)=(28-x²)²
16x²-256=784-56x²+x⁴
x⁴-72x²+1040=0
Let x²(blue area) = P
Therefore;
P²-72P+1040=0
P²-20P-52P+1040=0
P(P-20)-52(P-20)=0
(P-20)(P-52)=0
Therefore;
P ≠ 52
P = 20
And P = x² (blue area)
Therefore blue area (area inscribed square) is;
x² = 20 cm²
We appreciate you contacting us. Our support will get back in touch with you soon!
Have a great day!
Please note that your query will be processed only if we find it relevant. Rest all requests will be ignored. If you need help with the website, please login to your dashboard and connect to support