We know that the figure on the left, yellow in colour, has a contour 16.4 cm long and a surface area 10.5 cm² wide. How long is the outline and how extensive is the surface of the figure on the right, colored cyan?

The figure on the right has the same shape as the figure on the left, but has sides that are half as long. So its perimeter is half:  8.2 cm.

And the area?  Consider the figure on the right: rectangle A, double the size of rectangle B, contains four rectangles as large as B.  So if I divide the dimensions by 2 the area is divided by 4. In conclusion, if the area of ​​the yellow figure is 10.5 cm² that of the cyan figure is 10.5 /4 cm² = 2.625 cm².

Let's check the solution found by drawing a rectangle 2.625 cm² wide.  OK, the extent of the rectangle appears to be the same as that of the polygon.