Q1.
Look at the figures below and guess which one of them has a larger area.
Answer
By eye it is almost impossible to say — and that is exactly the point of the question. Shape b has sharp spikes that make it look bigger, while shape a is smooth and rounded.
The honest way to decide: trace each shape on transparent paper, place it on squared paper and count the squares using the four rules:
- one full square = 1 sq unit;
- more than half a square = 1 sq unit;
- exactly half a square = ½ sq unit;
- less than half a square = ignore it.
When this is done carefully, the smooth shape a turns out to cover slightly more squares than the spiky shape b — the spikes of b are thin, so they add very little region.
Why our eyes get fooled: we tend to judge by how far a figure spreads out, not by how much region it actually fills. A long thin spike adds a lot of boundary (perimeter) but very little area.