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Lesson 8 of 11

Walking the boundary

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8 min

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One line of the finished shape is not part of its edge.

Courtyard plus bed. The seam is inside.
Step 1 of 5
  1. Courtyard plus bed. The seam is inside.
  2. Count side one: 14 m.
  3. Count side two: 14 m.
  4. Count side three: 14 m.
  5. Count the arc: 22 m. Total 64.

The rule

Take the square courtyard of side 14 with its semicircular bed. The bed joins on the courtyard's fourth side. A seam is a line where two pieces join. That side is now an inside line. It is not part of the outer edge.

The boundary is every outer edge, each counted once. A seam is not on it.

The courtyard has three outer sides of 14. The arc is half of the circle's edge, 44, which is 22.

14 + 14 + 14 + 22 = 64 metres.

A 90° sector window of radius 7 is different. Its edge is two radii and one arc: 7 + 11 + 7 = 25. A card is 20 by 14 with a rounded end. The arc of 22 replaces one side of 14. Its edge is 20 + 14 + 20 + 22 = 76.

Drag the half circle onto a side of the courtyard. The side it joins becomes a seam. Read the edge.

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