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).