Geometric Reasoning: Perimeter by Translation

Methods in this video

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1. 1

   Parts of a line add up to the whole

   ▶ 1:29

   When to use it: A shape made of rectangles or squares with some sides unlabelled and marked not to scale, asking for a length, or needing hidden lengths before a perimeter or area.

   • Find one straight line and see which parts it is split into.
   • The parts add up to the whole line, so the missing part is the whole minus the known parts.
   • Check every corner: the width of the upright strip already takes up part of the line.
2. 2

   Push the sides to the frame

   ▶ 4:06

   When to use it: Finding the perimeter of a stepped right-angled shape (a staircase, a rectangle with pieces cut out, a shape with a strip added) with many sides unlabelled.

   • Push horizontal sides up or down and vertical sides left or right: the perimeter equals the frame's.
   • A notch's two walls cannot be pushed out, so add them; a cut-off corner adds nothing.
   • Same area does not mean same perimeter.