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Question id: 238. This question is similar to one that appeared in a IGCSE Extended paper in 2011. The use of a calculator is allowed.

### Mensuration Algebra

A circle is drawn inside a square so that it touches all four sides of the square.

(a) If the sides of the square are each $$k$$ mm in length and the area of the red shaded region is $$A$$ mm2 show that:

$$4A=4k^2-\pi k^2$$

(b) Make $$k$$ the subject of the formula $$4A=4k^2-\pi k^2$$

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