Step by step
The question
Question: two similar shapes have matching lengths 2 and 6, and the small area is 5: find the large area.
1 Length scale factor
Similar means the same shape: one is a bigger copy.
The scale factor k says how many times longer: the large one over the small one, 6/2, that is 6 divided by 2: 3.
2 Area factor
Area grows in two directions: k times k.
3 times 3 is 9.
Careful!
The area does not grow like the lengths.
It grows by k squared.
A square 1 by 1, made 3 times longer both ways, holds 9 little squares.
3 Use it
Going to the large one, we multiply by the factor: 5 times 9 is 45.
4 Check
Let's check: the large area divided by the small one is 9, which is k squared.
So it is right!
5 Type it in
The answer box takes 5 characters.
45 has 2.
It fits.
We type 45.
Let's look back.
First: length scale factor.
Then: area factor.
Then: use it.
Then: check.
Last: type it in.