SMT 2009 Geometry 2
Source:
December 28, 2011
geometryratiogeometric series
Problem Statement
The pattern in the fi gure below continues inward in finitely. The base of the biggest triangle is 1. All triangles are equilateral. Find the shaded area.[asy]
defaultpen(linewidth(0.8));
pen blu = rgb(0,112,191);
real r=sqrt(3);
fill((8,0)--(0,8r)--(-8,0)--cycle, blu);
fill(origin--(4,4r)--(-4,4r)--cycle, white);
fill((2,2r)--(0,4r)--(-2,2r)--cycle, blu);
fill((0,2r)--(1,3r)--(-1,3r)--cycle, white);[/asy]