# An Ant's Journey

Geometry Level 5

There is a $$4 \times 6 \times 18$$ inch cereal box lying on the floor. It was placed face down on one of its $$6 \times 18$$ inch face. An ant is located at one of the bottom corners of the box. It wants to reach the opposite bottom corner (of the $$6 \times 18$$ face on the floor), by crawling along the outside of the box, or on the floor. The length of the shortest such path is $$R$$ inches. What is the value of $$R^2$$?

Details and assumptions

The ant may not crawl under the box.

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