Math CentralQuandaries & Queries


Question from Aishwarya, a student:

A long time ago Mr gibson found an island shaped as a triangle with three straight shores of length 3km, 4km and 5km. He declared an exclusion zone around his island and forbade anyone to come within 1km of his shore. What was the area of his exclusion zone??

This question was answered but did not understand the explanation.

The key to this is to draw a really good diagram.

Start with the triangle. Now, note that near the corners, the boundary will be a circular arc. Near the sides it will be straight.

Color the parts of the exclusion zone that are nearest a corner one color. Color the parts nearest an edge another color. If you've done this right you should have three pieces of one shape and three of another.

Three will be easy to find the area of. The other three are easier if you move them around first and fit them together.

If you have really understood this, you should be able to find the area of a 1km exclusion zone around _my_ island, which is a convex pentagon with edges of 3, 4, 5, 6 and 7 kilometers. But its exact shape is secret.

If you have really, _really_ understood it, you should be able to find the volume of the exclusion zone around my asteroid, which is in the shape of a square pyramid with all edges 1 km long!

Good Hunting!

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