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

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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).