ABCDEF is a regular hexagon with sides of length h units. A square PQRS is drawn inside the hexagon, with PQ parallel to AB, SR parallel to ED, and vertices PQRS lying on FA, BC, CD and EF respectively.
The area of PQRS is 4 square units.
What is the exact value of h?
PS=2.
The regular polygons have a common center. Call this O.
Call the intersection of segments OF and PS = G.
GS=GO=1. Triangle SFG is a 30-60-90 so FG = sqrt(3)/3.
FO= 1+sqrt(3)/3
Triangle FOA is equilateral so
h = FA = 1+sqrt(3)/3
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Posted by Jer
on 2024-07-23 09:35:59 |
Simple analytical solution
