Square inside a semicircle such that one edge is on the semicircle and one side on the diameter

This question was uploaded on 06/12/21 on social media accounts.

Solution:

There are two right angled triangles:

\[a = \sqrt{4^2-3^2} = \sqrt7\]

By similar triangles:

\[\frac a4 = \frac x3\]

\[\Rightarrow x = \frac {3\sqrt7}4\]

\[\Rightarrow Area = x^2 = \frac {63}{16}\]