Are you sure?

Here's a seemingly easy maths question:

This was the MEI item of the month a while back. Analysis below.

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OK, hands up everyone that replied 30 cm^2. The actual answer is that the triangle can't possibly exist and therefore its area is undefined. Observe that there is a right angle in the top corner which means that we can draw the triangle inside a semi circle of radius 5cm like this:

This means that the maximum height of a triangle with a base (which is also the hypotenuse) of 10 cm is 5 cm so the triangle above can't exist. It is a lesson in caution.