A semi-circle is half of a circle. To find the area of the semi-circle, you should first understand how to find the area of a circle.
The general formula for the area of a circle is:

, so intuitively, the area of a semi-circle is just

Now, a diameter is twice the length of the radius, so we divide the diameter by 2, to yield the length of the radius, being 1 ft.
Substitute everything into the equation, and we get:


, which is about 1.5707... ft² ≈ 1.57ft² (nearest hundredth)