Explore the distances from an interior point of a polygon to its sides. What is the sum of these distances?
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Drag point H to new locations within the triangle to investigate the distances to each side. (Note: if point H is moved beyond the sides of the triangle, some of the measurements will disappear.) To change the size of the triangle, click-and-drag point A or point C.
Similarly, point G can be moved within the square, and points W and Z can be used to change the size of the square.
The Hide buttons will make the polygons and their measurements disappear. (This can be useful if you want to hide one shape while exploring a large version of the other.)
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You and Gilligan have become stranded on the desert island of Triangula, which is in the shape of a regular triangle. Gilligan is a lazy, incessant bore, so you’d like to build a hut far away from him. But you'd like easy access to each shore, so you also need to place your hut on the island so that the sum of the distances to each of the three shores will be as small as possible. Where should you place the hut?
Examine triangles of several different sizes.
How does the situation change if you are on a square island instead of a triangle?
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