GCSE Area and Perimeter

This revision guide will provide everything you need to know about area and perimeter for GCSE maths. You need to know a few rules to find the area of different shapes and how to deal with compound shapes. You also need to understand what perimeter means (then you can work out the perimeter of any shape).

Basically, the perimeter is the distance all the way around a shape. To calculate the perimeter simply start in one corner of the shape and imagine you’re moving along the side lengths around the shape. Add together all of the side lengths until you’re back at the corner you started at.

Area basically means the space inside a 2D shape. There are different rules to work out the area of different shapes. The main rules you need to know are set out below. Also make sure you check out our guide covering circles for the rule to work out the area of a circle.

Area of a Triangle

Area of a Triangle = 1/2 x Base x Perpendicular Height

Just remember that the ‘height’ in this formula is the perpendicular height (that means at 90 degrees to the base). You can see the perpendicular height set out on the diagram below.

Area of a triangle
Area of a Triangle = 1/2 x Base x Height

Area of a Rectangle

Area of a Rectangle = Width x Height

Area of a rectangle
Area of a Rectangle = Width x Height

Area of a Parallelogram

Area of a Parallelogram = Base x Perpendicular Height

Area of a parallelogram
Area of Parallelogram = Base x Perpendicular Height

Area of a Trapezium

Area of a Trapezium = 1/2 (a+b) x h

Area of a Trapezium
Area of Trapezium = 1/2 (a+b) x h

As you can see from the diagram above, a and b are the parallel sides of the trapezium and h is the perpendicular height. The formula for the area of a trapezium looks a little complicated at first, but once you’ve used it a few times you’ll soon know it off by heart.

Compound Shapes

Compound shapes are simply shapes made up of two or more recognisable shapes stuck together. To find the perimeter of a compound shape you need to carefully work out all of the side lengths and add these together.

To calculate the area simply split the compound shape into its constituent regular shapes and use the formulas set out above to work out the area of each shape. Finally, just add together each of the areas you’ve worked out to get the total area of the whole compound shape. Take a look at the example below. We’re going to work out the perimeter and area of this compound shape.

Compound Shape
Here’s a commonly used compound shape. It is made up of two rectangles stuck together.
Perimeter of a compound shape
Work out the missing side lengths.

Above I have calculated the size of the missing lengths by using the vertical and horizontal heights given. I can then add them all together to work out the perimeter: 10 + 5 + 4 + 7 + 6 + 12 = 44cm

Area of a compound shape

Next, to work out the area I have separated out the two rectangles. Always draw this onto the shape (as above) to help you. Calculate the area of both rectangles:

Then add these areas together for the total area of the compound shape:

So there you have it. In this guide we’ve explained how to calculate the perimeter of any shape and we’ve gone through the formulas to work out the area of the shapes you need to know for GCSE maths. We finished with a look at compound shapes. To build on this knowledge make sure you check out our guide on the area and circumference of circles. You can also contact us directly to ask any questions.

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