Perimeter of a rectangle

In your book, Maths Mela (Chapter 11), we find quick ways to work out perimeters. A square has four equal sides. For a square with sides of 5 cm, the perimeter is 5 + 5 + 5 + 5. That is 4 × 5 = 20 cm. So: Perimeter of a square = 4 × Length.

In a rectangle, the opposite sides are equal: two sides are the length and two are the breadth. So the perimeter is Length + Length + Breadth + Breadth, which is 2 × Length + 2 × Breadth. A rectangle 7 cm long and 4 cm wide has a perimeter of 2 × 7 + 2 × 4 = 14 + 8 = 22 cm.

The book asks for both the area and the perimeter of rectangles drawn on a 1 cm grid. Keep them apart: the area counts the squares inside (Length × Breadth, in square cm), and the perimeter measures the border (in cm). A square 3 cm by 3 cm has an area of 3 × 3 = 9 square cm and a perimeter of 4 × 3 = 12 cm. A rectangle 12 cm by 4 cm has an area of 48 square cm and a perimeter of 2 × 12 + 2 × 4 = 32 cm.

The book also asks you to draw rectangles with a perimeter of 26 cm. Half of the perimeter is one length and one breadth, so the length and the breadth must add up to 13 cm. A rectangle 8 cm by 5 cm works, and so does one 10 cm by 3 cm.