**Problem 1**

Given the length of each side of the
square ABCD is 1, find the shaded area of the crescent shaped loon ABC. Note:
the shape is bounded by semicircle ABC and the arc of a circle centered at
point D.

[Problem submitted by Luis Zambrano,
LACC Assistant Professor of Mathematics and Donald Hentschel,
LACC Professor of Mathematics.]

**Solution A for Problem 1:**

The shaded
area=area of the half circle ABC + area of _{}ADC-area of the quarter circle ACD

_{}.

**Solution B for Problem 1:**

We can separate the loon into two
areas: Semicircle ABC (with diameter AC = _{}units, radius R = _{}), and the 90° sector AC (with radius r = 1).