Question

How would you answer this question?

Answer 1

`[("Area of ABCD",:,"Area of shaded rectangle"),(125,:,8)]`

Explanation:

Let's call the area of the whole rectangle `A`. Since it has been split into the ratio 3:2, it has been split into 5 parts, so the area of the smaller rectangle is `(2A)/5`

That rectangle is split again in the same way, so the area of the smaller rectangle (not the shaded one by itself) is `2/5*(2A)/5=(4A)/25`

We do the same again for the shaded rectangle:
`A(2/5)^3=(8A)/125`

`[("Area of ABCD",:,"Area of shaded rectangle"),(A,:,(8A)/125),(1,:,8/125),(125,:,8)]`

Area of ABCD is 125 times bigger than 8 times the area of the shaded rectangle.