How to find the perimeter of a polygon - Math

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Question

Polygon

All segments of the polygon meet at right angles (90 degrees). The length of segment $\overline{AB}$ is 10. The length of segment $\overline{BC}$ is 8. The length of segment $\overline{DE}$ is 3. The length of segment $\overline{GH}$ is 2.

Find the perimeter of the polygon.

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Answer

The perimeter of the polygon is 46. Think of this polygon as a rectangle with two of its corners "flipped" inwards. This "flipping" changes the area of the rectangle, but not its perimeter; therefore, the top and bottom sides of the original rectangle would be 12 units long (10+2=12). The left and right sides would be 11 units long (8+3=11). Adding all four sides, we find that the perimeter of the recangle (and therefore, of this polygon) is 46.

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