The right(-angled) triangle is a Pythagorean triple: (3, 4, 5).

The semicircle is tangent to the hypotenuse of the right(-angled) triangle and secant to its base.

Then, the tangent line segments have the same length, 3.

Let $r$ be the radius of the semicircle. Then, we can draw $r$ tangent to the hypotenuse:

As the length of the base of the triangle is 4, we have:

Using the tangent-secant theorem,

So, the area of the semicircle is