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The sand heap

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

Bella

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