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| Math Central | Quandaries & Queries |
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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?
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?
Penny
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