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Six Discs

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Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the area enclosed by PQRS.

Pentagonal Area

Stage: 4 Short Challenge Level: Challenge Level:1
The area of the pentagon is the area of a rectangle of length $b$ and breadth $a$ plus that of a triangle of base $b$ and height $(c - a)$.

Hence $\frac {1}{2}b(a + c)$.

This problem is taken from the UKMT Mathematical Challenges.