Do You Know The Ins And Outs Of This Figure?

Geometry Level 2

The above shows a rectilinear figure (all its interior angles are either $90^\circ$ or $270^\circ$ only).

Calculate the perimeter of this figure.

The answer is 54.

2 solutions

Hung Woei Neoh
Jul 13, 2016

Imagine that the $5$ lines with known length are projected onto the remaining parts of the figure, like this

From the diagram, we can see that each of the $5$ lines occur twice on the composite figure.

Therefore, the perimeter is $2\times(5+5+4+6+7)=2\times27=\boxed{54}$

The same computation could also be explained by imagining someone walking around the perimeter once, starting with walking right from the top left corner. He/she walks right 5+6+7=18 units, and therefore must also walk left 18 units. Likewise he/she walks up 4+5=9 units, and therefore must also walk down 9 units.

Peter Byers - 4 years, 10 months ago

Michael Mendrin
Jul 6, 2016

Total perimeter is invariant. "Pull out" the figure to eliminate cul-de-sacs to get this figure as follows

This is probably the best method to solve such problems

Hritesh Mourya - 4 years, 11 months ago

Do You Know The Ins And Outs Of This Figure?

The answer is 54.

2 solutions

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