### Tri-split

A point P is selected anywhere inside an equilateral triangle. What can you say about the sum of the perpendicular distances from P to the sides of the triangle? Can you prove your conjecture?

### Areas and Ratios

What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.

### Six Discs

Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases?

# Weekly Problem 18 - 2006

##### Stage: 4 Challenge Level:
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.

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