Perimeter of staircase and notched figures

All the lines meet at right angles. The steps go across six, down four, across five, down three, across seven and down five centimetres. Find the perimeter. Try it first. Pause if you like. Perimeter follows the whole outside boundary, including the unlabelled base and left side. Watch the blue trace go all the way round. Can we move the step edges into straight sides without changing any of their lengths? Shift the sides out to the rectangle that encloses the figure. We move copies of the edges; the original figure stays in place. Slide the three across-steps upwards. Their lengths stay six, five and seven centimetres. Together, they span the whole length. Length of the figure equals six centimetres plus five centimetres plus seven centimetres, which equals eighteen centimetres. Slide the three down-steps to the right. Their lengths stay four, three and five centimetres. Together, they span the whole breadth. Breadth of the figure equals four centimetres plus three centimetres plus five centimetres, which equals twelve centimetres. Perimeter equals eighteen centimetres plus twelve centimetres plus eighteen centimetres plus twelve centimetres, which equals sixty centimetres. The perimeter of the figure is sixty centimetres. Every edge kept its length. The perimeter is unchanged. This does not mean that the two figures have the same area.

The rectangle is twenty-two centimetres long and fourteen centimetres wide. Its bottom notch is six centimetres wide and five centimetres deep. Find the perimeter. Try it first. Pause if you like. Follow the actual boundary. At the notch, it goes up, across and down again. Both upright edges are exposed, so both belong to the perimeter. Will shifting the horizontal edge fill the bottom gap and account for every edge of the notch? Shift the sides out to the enclosing rectangle. The six-centimetre horizontal edge slides down and fills the six-centimetre gap. Perimeter of the enclosing rectangle equals twenty-two centimetres plus fourteen centimetres plus twenty-two centimetres plus fourteen centimetres, which equals seventy-two centimetres. The two sides of the notch run back on themselves and do not shift, so they are added on. Each is five centimetres long. The six-centimetre width is already included along the bottom. Only the two five-centimetre depths are extra. Perimeter of the figure equals seventy-two centimetres plus five centimetres plus five centimetres, which equals eighty-two centimetres. The perimeter of the figure is eighty-two centimetres. A staircase shifts into the enclosing rectangle. A notch leaves two extra depths to include.