Using Simple Formulae

The perimeter of a shape is the total distance around its outside edge. Imagine walking all the way around a rectangle, first along the long side, then the short side, then the long side again, then the short side again. The distance you walked is the perimeter.

A rectangle has two long sides (the length) and two short sides (the width). A handy formula puts this into symbols: P = 2 × (l + w). The P stands for perimeter, the l for length, and the w for width.

Here is how to use it. Say a rectangle has a length of 10 cm and a width of 4 cm.

1. Add the length and the width: 10 + 4 = 14. 2. Double the total, because each side appears twice on a rectangle: 14 × 2 = 28. 3. The perimeter is 28 cm.

Why double the sum instead of adding all four sides one by one? Because the two long sides are equal and the two short sides are equal, so 2 × (l + w) does the same job in fewer steps.

A formula is a shortcut that tells you how to find something from numbers you already know. Once you know a formula, you can plug in new numbers again and again.

Here are some simple formulas that are useful to remember.

Perimeter of a rectangle: P = 2 × L + 2 × W. That means two times the length plus two times the width. It gives the same answer as P = 2 × (L + W), because doubling the whole sum is the same as doubling each part and adding.

Perimeter of a square: P = 4 × s, where s is the side length. A square has four equal sides, so you just multiply one side by 4.

Area of a rectangle: A = L × W. Multiply the length by the width and you get the space inside the shape.

A formula only works if you put the numbers in the right places. When you see P = 2 × (L + W), the brackets tell you to add L and W first, before you double. Try each formula with easy numbers first to check that you are using it correctly.

When a formula has more than one step, the order you do things in matters. Mathematicians all agree on one order, so everyone gets the same answer.

1. Work out anything inside brackets first. 2. Do multiplies and divides next. 3. Do adds and takes-away last.

This matters a lot when you substitute numbers into a formula. Take P = 2 × (l + w) for a rectangle with length 9 and width 3.

If you add first, you get 9 + 3 = 12, then 12 × 2 = 24. Correct!

If you multiplied first by mistake, you would get 2 × 9 = 18, then 18 + 3 = 21, which is wrong.

So the rule is simple: brackets first. Any time you see a formula with brackets, calm down the part inside them before doing anything else. Take it one step at a time and write each step down.