Imaginary Line

Yesterday I heard myself say something havent said in decades

Draw an imaginary line

While saying that I drew a dotted line joining the opposite sides of a rhombus - parallelogram. When I explained the parallel lines, we agreed that the parallel lines meet at infinity, where there is a pirate.

When I said

Draw an imaginary line

My daughter said she did.
She did draw the imaginary line in her head.

We started with a triangle with unit area.
It was easy to say the parallelogram has 2 units area.

Then came a hexagon. 6 . Great.

Imagine the triangle doing a hop around each side. 6 sides. 6 units of area

We are learning surveying here. I remember high school problems where we had to split the random shapes into trapeziums. (I think I just figured why trapeze is called a trapeze. when it swings in either direction, it makes that shape. )

Then came a huge shape. We saw that it was symmetrical.
If we solve half the problem then, we will know the other.
We went around tracing the given shapes - triangle or rhombus into the half of the random shape and worked out the answer. Luckily, the answer was written but it didnt show, how that was arrived at.

We traced the actual shape on the back of the paper, so we could freely go about solving the problem. After having solved the problem, I recalled Einstein not being happy with just one solution but looking at the haystack for all the needles that mght be there.

We realised that there are other symmetries, so the problem could be solved differently. Finding alternate ways of solving a problem, is a validation of your prior solution.

We learned to not freak out at a big problem

 Divide and Rule.