Any help would be greatly appreicated! 


1. Let A be the center of equilateral triangle DEF. A dilation, where the center is A, with scale factor -1/3, is applied to obtain triangle D'E'F'. Let P be the area of the region that is contained in both triangles DEF and D'E'F. Find P/[DEF].


2. Just like before, we have DEF and A as the center. However, this time the dilation (still centered at A) has a scale factor of -4/3. H is the region in both DEF and D'E'F'. Find H/[DEF].







I tried to solve this using information found in other questions similar to these, but I just don't get how to get the hexagons P and H. Thank you very much! smiley

 Feb 24, 2021

[ABC] = √3 / 4 * AB2

Calculating the area of a hexagon:

AC = 3        MC = 1.5        A'B' = 4         C'N = √12         QN = 1/3(C'N)

CQ = cos30º * MC

CN = CQ - QN

DN = tan30º * CN

[CDE] = DN * CN

Hexagon area = [ABC] - 3[CDE]

 Feb 24, 2021

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