# Area

This post will discuss area and how it applies to concreting. It will also explain how to calculate the area of different shapes which can be applied practically when working.

## Area and Concreting

Almost everything in concreting is to do with area. We construct, or lay, “areas of concrete”. A concrete slab is an area where concrete is laid.

Many of the materials we use to construct concrete areas will be calculated or thought about in terms of area.

Understanding how to find the area of different shapes will make it faster, easier and more accurate to price, start and finish a concreting job.

Important

```When we work out the area of a shape, we usually will talk about the area size in square metres.

square metres is written as: m2, m2 or sqm```

## Square

A true square’s area can be found by raising the value of square’s side Length by the power of 2.

`Length^2`

## Rectangle

A rectangle’s area can be found by multiplying the rectangle’s Length by its Width.

`Length * Width`

## Triangle

A triangle’s area can be found by multiplying the Base by the Perpendicular Height and then multiplying by 0.5

Math Tip

`Multiplying by 0.5 halves a value.`
`Base * P. Height * 0.5`

## Circle

The radius of a circle is the distance from the center to the edge of the circle. It is half the value of the circle’s diameter.

A circle’s area can be found by multiplying Pi (3.14) by the circle’s Radius raised by the power of 2.

`3.14 * Radius^2or3.14 * Radius * Radius`

## Trapezoid

A trapezoid is a square or a rectangle with 1 or 2 angled sides.

By understanding and using the trapezoid’s area formula it saves you calculating the triangles separately.

`(Length + Width) * P. Height * 0.5`

## Examples

### Waffle Pod – Square

A waffle pod is 110cm on both its length and width. The area that a waffle pod takes up can be found using the Area of a Square Formula.

Remember

```If we square a number, it means we multiply it by itself.

This is also called raising by the power of 2 or to the power of 2.
When we write this operation, it looks like: ^2

We can raise to the power of different numbers as well. So to the power of is indicated by the ^ character.

On a calculator you will see a button that says xy.
This button is the to the power of button.```
```Length^2

Length = 110cm

Length^2
=110^2
= 12100cm2

Now change the Length into metres instead of centimetres...
Length = 1.1m
Length^2
= 1.1^2
= 1.21m2 ```

The area of a 110cm waffle pod in square metres is 1.21m2

### Viscrine (Black Plastic) – Rectangle

A roll of viscrine is 50m long. It folds out to be 4m wide. Let’s use the Area of a Rectangle Formula to find how much area a whole roll can cover:

```Length * Width

Length = 50m, Width = 4m

Length * Width
= 50 * 4
= 200m2```

The total area a full roll of viscrine will cover is 200m2

### Mesh – Triangle

We are making someone’s driveway wider.

The shape will be a triangle and the mesh needs to be cut to suit the shape. The mesh size needs to be a triangle with one side 2.2m and the other side is 4.8m. Work out the area that the mesh piece will be:

`Base * P. Height * 0.5`

The Base will be the Length. The Perpendicular Height (P. Height) will be the Width. Therefore:

```Base = Length, P. Height = Width
Length = 4.8m, Width = 2.2m

Base * P. Height * 0.5
= 4.8 * 2.2 * 0.5
= 5.28m2```

The triangular piece of mesh will have an area of 5.28m2.

## Exercises

### 1.

Your uncle wants to have a patio laid at his house. The area he wants to make the patio is a square shape with sides that are 6m.

What is the area of the proposed patio?

### 2.

Find the area of the shape shown above. Hint: you can use rectangle & triangle formulas, or use the trapezoid formula.

### 3.

The plan above shows a round-about. The inner circle has a 5m radius and the outer circle has a 15m radius. If we are going to concrete the roundabout (like a donut!) How many square metres will it be?

Hint

`The 5m radius circle will not be concrete.`