Scale and size
Make a whole object bigger by some factor. What happens to its lengths, its area and its volume, and how can that measure something you cannot reach?
Where you are 3 inside
What this area is about
A scale copy multiplies every length by one number, the scale factor k. Lengths are the easy part. Area and volume do not grow by k. And because matching lengths keep one ratio, a small triangle you can measure tells you a height you can never reach.
How these fit together
The rule for lengths. Scale factor multiplies every length: sides, diagonals, heights and perimeter all get multiplied by the same k.
The result for area and volume. Scale factor, area and volume shows that area is multiplied by k^2 and volume by k^3, because an area needs two lengths and a volume three.
An application. Measuring what you cannot reach finds the height of a tree or a flagpole from a small triangle you can measure and a large one with the same angles, using a shadow, a mirror or an angle.
A path through it
Lengths first, then area and volume, which also needs surface area. Measuring what you cannot reach does not rest on the other two; it needs similar triangles, a protractor and angles of elevation, so it is high school work (grades 9 to 12).
Finish here and you can predict how much paint, carpet or material a bigger or smaller copy needs, not just how long its sides are.