A very loose definition of area is ‘how much stuff you could fit on the floor’. Depending on how big the shape you’re looking at is, you measure area in square centimetres (cm2), square metres (m2) or (unusually) square kilometers (km2).

Really easy rectangles and squares

Working out the area of rectangles is very straightforward: all you do is multiply together the height of the rectangle by its width.

If you’re dealing with a square, you know the height and the width are the same, so you just multiply the length of the side by itself.

Trickier triangles

Triangles are a little more difficult to work out, but not all that difficult. Here are the steps you follow to find the area:

1. Find the length of the base of the triangle, the distance across the bottom.

2. Find the height of the triangle, the distance from the base to the top.

4. Halve your answer from Step 3. This is the area of the triangle.

If you tilt your head and narrow your eyes a bit, you may be able to see why this is the way to do it. A triangle is half as big as a rectangle with the same width and height, so its area is half of the rectangle’s area.

Also, if you’re a remembering-formulas kind of person, you may like to remember ‘half base times height’ as the formula for the area of a triangle.

Combining rectangles

It’s pretty unusual to get a question as simple as ‘find the area of this rectangle’ in a test. Most tests like to spice it up a bit and bundle two or more rectangles together and ask you to find the total area. You need to think a little harder for this kind of question, but the steps are pretty logical:

1. Split your complicated shape up into two rectangles (or more, if you need to).

2. Work out the height and width of each rectangle. You may need to add or take away some given lengths from each other to find all the information you need.

3. Work out the area for each rectangle – multiply the width of each rectangle by its height.

4. Add up the areas you worked out in Step 3.

It doesn’t matter how you split the rectangle up, you still end up with the right area!

Surface areas

A variation on the compound rectangle is the surface area question. If the question asks you for the surface area of a three-dimensional shape (usually a box), it’s really asking how much wrapping paper you would need to wrap it up.

Oddly enough, that’s exactly how you work out the surface area of any 3D shape:

1. Find the area of each face of the shape. All of the faces will be simple shapes, most likely rectangles but possibly triangles as well. Remember to include the faces hidden at the back of the drawing.

2. Add up all of the areas you worked out in Step 1. This is the total surface area.

Fiddling with formulas

The last kind of area question you’re likely to see involves using a formula to find the area of a complicated shape. These look a bit intimidating, especially if you have bad memories of algebra from school, but if you take a deep breath and approach the problem systematically, you can pick up easy marks here.

So, taking it one step at a time:

1. Figure out which letter stands for which quantity – the question usually says what stands for what directly underneath the formula.

2. Rewrite the formula, replacing each letter with the value it represents – so if you know h is 5, you replace all of the hs in the formula with 5. If there are two values next to each other without a +, –, x or ÷ in between them, and there ought to be a x, write it in!

3. Work out the sum you just figured out using the BIDMAS rules – work out what’s in the brackets first, then any indexes (powers), then any multiplications or divisions, then additions or subtractions.

An index is a little number above and to the right of another number, like this: 42. What this means is ‘multiply a list of two 4s together’, or 42 = 4 x 4 = 16. In the same way, 53 = 5 x 5 x 5 = 125.