Two squares share a vertex. Three other vertices form a triangle, of which one side length is given. What is its area?

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## Solution

The coloured area is 2.

First acknowledge that ∠FBC equals ∠EBA. Using SAS, it is clear that ▵FBC is congruent to ▵EBA. Therefore FCD is a straight line.

Now using AAS, ▵FBC and ▵FGH are also congruent, making altitude HG having length 2. The required area follows.

## Poem

The sand pile

Is measured by grains

It is coarse or fine

Perhaps beach sand

Or muddy quicksand

But to fall asleep

The sandman will come

And tell some fables

To built castles in sand

Sand castles will crumble

In sand heaps

And end