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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?

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Great Squares

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

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Square Areas

Can you work out the area of the inner square and give an explanation of how you did it?

Mid-point Area

Stage: 3 Short Challenge Level: Challenge Level:1

Rectangle with Triangle PMR
$M$ is the midpoint of the side of the rectangle, so $RM$ has length $2$ units.

\begin{eqnarray} \text{Area of Triangle } PMR & = & \frac{1}{2} \times \text{base} \times \text{height} \\ & = & \frac{1}{2} \times 2 \; \text{units} \times 3 \; \text{units} \\ &=& 3 \; \text{square units}\end{eqnarray}

This problem is taken from the UKMT Mathematical Challenges.