Solve for x, round to hundredths place

Given: m∠ adb = m∠cdb ad ≅ dc prove: m∠ bac = m∠bca lol

In the figure below, ∠dec ≅ ∠dce, ∠b ≅ ∠f, and segment df is congruent to segment bd. point c is the point of intersection between segment ag and segment bd, while point e is the point of intersection between segment ag and segment df. the figure shows a polygon comprised of three triangles, abc, dec, and gfe. prove δabc ≅ δgfe.

The midpoints of the sides of the large square are joined to form a smaller square. what is the area of the smaller square