Area and perimeter: Triangles and quadrilaterals

In a nutshell

The perimeter and area are unique properties of every shape. The perimeter and area of triangles and quadrilaterals can be calculated using different formulae.

Perimeter

The perimeter is the distance around the outside of a $2d$ shape. This is the sum of all the lengths of the outer sides of a given shape.

Example 1

What is the perimeter of the shape below?

Maths; Measures; KS3 Year 7; Area and perimeter: Triangles and quadrilaterals

Calculate the sum of all the outer sides.

$4+3+5+2 = 14m$

Therefore, the perimeter is $\underline{14m}$ .

Note: Ensure all the units are the same for each length before adding them together.

Area

The area is the size of a shape's surface. There are different formulae to calculate the areas of different shapes. You will need to learn the following formulae.

SHAPE	FORMULA	ILLUSTRATION
Triangle	$\text{Area}=\frac{1}{2}\times\text{base}\times\text{perpendicular\,height}$ $A=\dfrac{1}{2}bh$	$b$
Rectangle	$\text{Area}=\text{length}\times\text{width}$ $A=lw$
Parallelogram	$\text{Area}=\text{base}\times\text{perpendicular\,height}$ $A=bh$
Trapezium	$\text{Area}=\dfrac{1}{2}\times(a+b)\times\text{height}$ , $A=\dfrac{1}{2}(a+b)\times h$

Example 2

What is the area of the triangle below?

Maths; Measures; KS3 Year 7; Area and perimeter: Triangles and quadrilaterals

Identify the formula for the area of a triangle.

${Area}=\dfrac{1}{2}\times{base}\times{perpendicular\,height}$

Identify the relevant values.

$\begin{aligned} &{Base} &= 4cm \\&{Perpendicular \ height} &= 4cm \end{aligned}$

Place the values into the formula.

${Area}=\dfrac{1}{2}\times 4 \times 4$

$\underline{{Area}=8 cm^2}$

Note: Area is measured in square units.