Star - Part 4
Geometry
Level
1
The above image shows a 5-pointed star ABCDE, and a regular pentagon FGHIJ.
If the star has a (outside) perimeter of 50, and the pentagon has a perimeter of 30, what is the perimeter of AGFJ?
30
32
34
40
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1 solution
The perimeter of AGFJ= (lengths of) AH+HG+GF+FJ+JI+AI. AH and AI are sides of triangles, which have length 50/10=5. HG, GF, FJ, and JI are sides of the pentagon (or bases of triangles), which have length 30/5=6. The perimeter of AGFJ=5+6+6+6+6+5=34.