Picture the school yard from above. The caretaker wants to put a new fence all the way around the edge of it. Before any fencing can be ordered, somebody has to work out how much fence is needed.

Three labelled shapes are on screen, showing the sides of a rectangle, a regular pentagon and an L-shaped plot. The diagrams use centimetres to stay small, but the thinking is the same for a real yard in metres. Watch how we find the distance all the way round each one.

Rectangle first: sides 4.5 cm and 2.5 cm. Add all four, 4.5 + 2.5 + 4.5 + 2.5 = 14 cm, or double each matching pair.

Regular pentagon next: five equal sides of 3.2 cm. Same length five times means 3.2 x 5 = 16 cm.

L-shape last. The sides you can see are 6 cm, 5 cm, 2 cm, 3 cm and 4 cm. The top edge has no label. Match it to the two bottom pieces, 5 + 3 = 8 cm. Then add every side once round: 8 + 4 + 3 + 2 + 5 + 6 = 28 cm.

Let's draw an irregular shape on the board and measure each side together, then add them all up to find the perimeter. First, count how many sides the shape has so we know how many numbers to expect, then we'll go round one side at a time, saying each length out loud before we add it on.

Today we work through these perimeter problems together, getting trickier as we go:

• Find the perimeter of a regular hexagon with each side 4 cm.
• Find the perimeter of an L-shape from its labelled sides.
• Find the perimeter of an L-shape that has one side missing — work out the missing side first.
• Find the perimeter of a regular pentagon with each side 6 cm.
• Stretch: the perimeter of a square is 24 cm. How long is each side?

Today you learned to

• Find the perimeter by adding every side once around a shape
• Use a multiply shortcut when sides repeat, like in a regular shape
• Work out a missing side before completing a perimeter

Coming up

Next we move from the distance around a shape to the surface inside it: finding the area of rectangles and compound shapes.