What is Area?
Area is the amount of space taken up by the total surface of a shape. To find the area of a shape, we need to know exactly how many square units will fit inside it. Here are two ways to do this.
1. Count the Squares
The first is to count how many squares will fit into the shape, like this:
Did you notice? Even when the shape changed, the total number of square units was the same for the rectangle. All these shapes have an area of six square units.
A handy way of modeling the concept of area is to cut out some squares cards and see how many will fit inside a simple shape.
When you are calculating area, your measurements should be in the same units. If you measured in centimeters, for example, then your answer will be written in centimeters squared (centimeters multiplied by centimeters) .
2. Use a Formula
Counting squares can work well for small, simple shapes but it gets tricky if the shape is very large or more complex. Using formulas and some key facts we can find the area of many different shapes, including:
The formula for the area of a rectangle is length multiplied by width.
- Area = Length × Width
- Area = 5 × 10
- Area = 50 cm2
The formula for the area of a triangle is base multiplied by height divided by two.
- Area = (Base × Height) / 2
- Area = (10 × 5) / 2
- Area = 50 / 2
- Area = 25 cm2
Did you know that the area of a triangle is half of the rectangle (or parallelogram) that could be made by doubling the triangle?
For the area of a circle, all you need to know is the length from the center of the circle directly to the outside edge, the radius. The formula for the area of a circle is π (Pi) multiplied by the radius squared. Pi is a special number that equals 3.14 (rounded), radius squared means radius multiplied by radius.
- Area = π × Radius2
- Area = 3.14 × 5 × 5
- Area = 3.14 × 25
- Area = 78.5 cm2
Area in Real Life
If you are working with a two dimensional shape, there is a good chance that area will be a part of your thinking.
- Covering a book
- Making a quilt
- Painting a room
- Ordering tiles
- Buying land
- Mowing a lawn