Perimeter

Walk once round the edge of a field and come back to where you started. The distance you walked is the field's perimeter. The perimeter of a closed figure is the distance covered when you go along its boundary once, all the way round. For a polygon, a closed figure made of straight sides, the perimeter is simply the sum of the lengths of all its sides.

When a shape has many sides, go round it letter by letter: AB, then BC, then CD, and so on, writing each length as you go. That way you never miss a side or count one twice.

Take rectangle ABCD, 12 cm long and 8 cm broad. Its perimeter is AB + BC + CD + DA. Opposite sides of a rectangle are always equal, so this is 12 + 8 + 12 + 8 = 40 cm. A shortcut: add the length and the breadth once, then double it.

• Perimeter of a rectangle = 2 × (length + breadth) = 2 × (12 + 8) = 2 × 20 = 40 cm.

Debojeet wants to put coloured tape all round a square photo frame of side 1 m. All four sides of a square are equal, so instead of 1 m + 1 m + 1 m + 1 m he can multiply:

• Perimeter of a square = 4 × side = 4 × 1 m = 4 m of tape.

For a triangle, add its three sides. A triangle with sides 4 cm, 5 cm and 7 cm has perimeter 4 + 5 + 7 = 16 cm.

Closed figures with all sides equal and all angles equal are called regular polygons: the square, the equilateral triangle (three equal sides, three equal angles), the regular pentagon, and more. For these, multiply the number of sides by the length of one side. Perimeter of an equilateral triangle = 3 × side, so one with sides of 5 cm has perimeter 15 cm. A regular octagon has 8 equal sides, so with sides of 3 cm its perimeter is 8 × 3 = 24 cm.