Count and Compare Sides and Corners of Shapes

Every flat shape is built from straight lines and points. The straight lines are called sides, and the points where two sides meet are called corners. Counting these sides and corners carefully is one of the easiest ways to tell shapes apart and to compare one shape with another.

A side is a straight edge of a shape. A corner (sometimes called a vertex) is the sharp point where two sides join together. To count them accurately, it helps to trace around the shape slowly with a finger, tapping each side once and each corner once so nothing gets counted twice or skipped.

To count sides, start at any point on the shape and move your finger along each straight edge, saying a number out loud every time you reach the end of one side and start the next. A triangle has 3 sides, and a square, rectangle, or any four-sided shape has 4 sides. This is exactly what people mean when they talk about a shape with 4 sides and 4 vertices.

It helps to already know the names of common shapes before counting, since knowing that a shape is called a rectangle or a pentagon gives a quick clue about how many sides to expect. If you need a refresher on shape names first, see Name and select the 2D shape.

Corners are counted the same way, but instead of tapping along the edges, tap each point where two sides meet. A triangle has 3 corners, a square has 4 corners, and a pentagon has 5 corners. Notice that for these straight-edged shapes, the number of sides and the number of corners always match, because every side needs exactly two corners to start and end it, and each corner is shared by two sides.

A circle is different: it has no straight sides at all, just one curved line, so it has 0 sides and 0 corners.

Once you can count sides and corners on one shape, comparing two shapes is just a matter of counting both and seeing which number is bigger or smaller. This is a handy way to sort shapes without even worrying about their names.

Here the hexagon has 6 sides and 6 corners, while the pentagon has only 5 of each. Since \(6 > 5\), the hexagon has more sides and more corners than the pentagon. Comparing shapes this way also comes in handy when you put smaller shapes together, since joining shapes can change the total number of sides and corners in the new figure. You can explore that idea further in Compose 2D shapes.

Which has more corners: a square or a triangle? First count the square's corners by tapping each point: 1, 2, 3, 4, so the square has 4 corners. Then count the triangle's corners: 1, 2, 3, so the triangle has 3 corners. Since \(4 > 3\), the square has more corners than the triangle. The same comparison works for sides, since the square also has more sides than the triangle.

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• Kindergarten