Math CentralQuandaries & Queries


Question from Kristen, a parent:

He trained his snail, Rondo, to crawl around a 6 x 8 rectangle. Rondo stayed exactly 3 cm from the rectangle at all times. What is the total area that Rondo surrounded with his slime trail?

Hi Kristen,

Did you draw a diagram?

snail trail

When Rondo crawls around the rectangle he surrounds a region as in my diagram.

The region includes the original rectangle. What is its area?

It includes four rectangular strips, 3 cm wide (blue in my diagram). What is the area of the four strips?

Finally it includes four quarter circles of radius 3 cm. What is the area of the four quarter circles?

What is the total area?


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