#### Answer

A$\approx$42.33

#### Work Step by Step

An inscribed angle that intercepts a semicircle is always a right angle. Therefore angles D and B are right angles.
AD$^2$=AC$^2$-CD$^2$
AD$^2$=100-16
AD=$\sqrt {84}$
BA$^2$=AC$^2$-BC$^2$
BA$^2$=100-36=64
BA=8
A=.5(4)($\sqrt {84}$)+.5(6)(8)
A=2$\sqrt {84}$+24
A$\approx$42.33