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Chapter Overview

Maths

Exam board

Pearson Edexcel

Number

Algebra

Graphs

Ratio proportion and rates of change

Shapes and area

Angles and geometry

Trigonometry

Probability

Statistics

Maths

Area and perimeter: Formulae

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Area and perimeter: Formulae

​​In a nutshell

The perimeter and area of triangles and quadrilaterals can be calculated with their own formula. These formulae can also be applied to finding the area and perimeter of compound shapes.


Area and perimeter - definitions

The perimeter of a shape is the sum of the lengths of the outer sides of the shape.

The area of a shape tells you the size of the surface of the shape.



Area formulae

These are the following formulae you need to know.


​​shape

formula

illustration

Triangle

Area=12×base×perpendicular height\text{Area}=\frac{1}{2}\times\text{base}\times\text{perpendicular\,height}​​


​A=12bhA=\frac{1}{2}bh​​
​
Maths; Shapes and area; KS4 Year 10; Area and perimeter: Formulae
bb​​

Square

Area=length2\text{Area}=\text{length}^2​​


​A=x2A=x^2​​

​​

Maths; Shapes and area; KS4 Year 10; Area and perimeter: Formulae
​xx​​

Rectangle

Area=length×width\text{Area}=\text{length}\times\text{width}​​


​A=lwA=lw​​
Maths; Shapes and area; KS4 Year 10; Area and perimeter: Formulae

Parallelogram

Area=base×perpendicular height\text{Area}=\text{base}\times\text{perpendicular\,height}​​


​A=bhA=bh​​

​

Maths; Shapes and area; KS4 Year 10; Area and perimeter: Formulae

Trapezium

Area=12×(a+b)×height\text{Area}=\frac{1}{2}\times(a+b)\times\text{height},


A=12(a+b)×hA=\frac{1}{2}(a+b)\times h​​


where aa and bb are the lengths of the two parallel sides.
Maths; Shapes and area; KS4 Year 10; Area and perimeter: Formulae

​

Area and perimeter problems

You can use the formulae for the areas and perimeters of triangles and quadrilaterals to solve problems involving more complex shapes.



Example 1

In the diagram below, let a=5m,b=9m,c=4ma=5m,b=9m,c=4m