### Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

### Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

### 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?

# Pentagonal Area

##### Stage: 3 and 4 Short 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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