What is area?
Area means the space a two-dimensional shape takes up. We can start by using unit squares, and count them up, which is straight forward with shapes such as rectangles and squares.
The area of rectangles
Now that we can see what area actually means, we can use units of measurement to work out the area of rectangles and squares. Actually, squares are special rectangles, so you can use the same approach and rule for both! Need a refresher about the properties of shapes? This link is a useful reminder. Let's see how to calculate the area of rectangles and squares.
More?
Need some more help with the area of squares and rectangles? Here are some links that might be useful:
- Finding the area of shapes using unit squares
- Finding the area of area of squares and rectangles using the rule
- Real problems involving the area of squares and rectangles
Worked Example
Question 1
Find the area of the attached figure.
The area of triangles
In this video, we look at how a triangle's area can be worked out by looking at its related rectangle. This is pretty cool, and it means you can remember the rule for the area of a rectangle, and use it for other shapes too!
Worked Example
Question 2
Find the area of the triangle shown.
A right-angled triangle is illustrated with its base measures $8$8 m and its height measures $7$7 m. The hypotenuse, side opposite to the right angle indicated by a small box, is not labeled.
Want to see yourself how a triangle and rectangle are related? Check out the mathlet below to see for yourself. Drag the vertices of the triangle to change its shape and then slide the slider to see how it turns into a rectangle.
The area of parallelograms
Just like triangles, we can construct a rectangle around every parallelogram. This time, the area of a parallelogram is the same as the area of its associated rectangle. That is fabulous, because you don't have to remember another rule for area! Check it out.
Worked Example
Question 3
Find the area of the parallelogram shown.
A parallelogram is shown. The base measures 21cm. The height measures 20 cm, as represented by a vertical dashed line inside the parallelogram which is drawn perpendicularly from the top side to the bottom right vertex.
Putting it all together
Now, after all of that, you don't want to have to remember too many rules! Let's see them together, so we can see how the rule for the area of a rectangle is the one to remember.
What can we do with all of this information?
If you know the area of a shape, and one of the dimensions (or none for a square), you can work out missing dimensions. In the final video you'll see how to work backwards to find missing dimensions, and then how to solve a problem with a mural that needs decorating.
Dimensions and area
In this applet, you can see how the area, base and height are related for triangles. Play around and see if you can work out the missing values.
The area of a rectangle can be used to help find the area of a square, triangle and parallelogram. Learning that rule is the first step.