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Area
Area
Area is the space a shape occupies. In real life situations, you will use area to work out how much carpet you need, or the amount of grass seed needed to replace a lawn for example.
Lesson plan
Today's lesson
Lesson plan
- Area of rectangles
- Area of triangles
- Compound and complex shapes
- Home work
Rectangles and triangles
In an exam, you will need to work out the area of a given shape. This shape is likely to be made up of a number of different shapes. Once you know the basics of how to work out each shape, you can work out more complicated areas.
We will look at circles separately.
Area of Rectangles and triangles
Area of a rectangle
Working out the area of a rectangle (or square) is easy - multiply length by width! We give our answer in 'square' units: this is indicated by a small '2' hanging above the measurement unit eg m .
Rectangles
2
Have a look at these:
8cm x 3cm = 24cm
2
Examples
32m x 20m = 640m
2
We use the '2' after m to indicate 'squared'; this is just to show we are dealing with space inside.
Area of triangles
Working out the area of a triangle is also pretty simple. If you can do rectangles, you can work out triangles! This is because a triangle is just half of a rectangle. So to work out the area of a triangle, follow the same rules as for rectangle (base x height) and then half it. Easy!
Triangles
Look at these:
5cm x 3cm = 15cm ÷ 2 = 7.5cm
2
Examples
12cm x 20cm = 240cm ÷ 2 = 120cm
2
What to expect in exams
Exam style questions
You should know by now that exam questions are rarely simple! Once you have worked out an area, you may be expected to do something with it -work out how many trees to plant for example. Have a look at these sample questions and how to work them out:
Example 1
This is a tricky one for a number of reasons:
1. No calculator!
2. more than 1 area
3. Multi-step question.
Have a go before looking at the steps to solve.
This is how to solve this one:
2
How to solve
1. Work out the area of the outside shape: 12 x 14 = 168cm
2. Work out the area of the inside shape: 8 x 10 = 80cm
3. Take the inside away from the outside: 168 - 80 = 88cm
Done! The frame area is 88cm
2
Example 2
Another difficult one, because of the steps needed.
1. Working out area
2. How many chickens fit?
Again, try it before you look at the solution.
Solution:
2
1. Find the area of the rectangle: 18 x 8 = 144m
2. Divide the area by the space each chicken needs: 144 ÷ 3 = 48
Problem solved! There is space for 48 chickens.
How to solve
Example 3
This looks scary because of the triangle, but it works in exactly the same way as the first example (photo frame).
How to:
2
1. Work out the area of the garden: 8 x 12 = 96m
2. Work out the area of the vegetable patch: 5 x 4 = 20 ÷ 2 = 10m
3. Take the vegetable patch away from the garden: 96 - 10 = 86m
Done! The grass has an area of 86m
How to solve
2
Area of compound shapes
When you come across area in exams, the chances are you won't see just a rectangle or a triangle. The shapes will be complicated, usually combinations of shapes put together. Don't panic! Complex shapes are pretty easy once you know the secret.
Compound shapes
Area of complex shapes
Working out complex shapes
Have a look at this shape. We know that area is length x width, but this is not a simple shape! How do we work this out? The easiest way? Split it into simple shapes.
Steps
1. Split the shape into 2 rectangles.
2. Work out each rectangle.
3. A: we can work out the missing side because 6cm-4cm = 2cm. Now area. 2 x 2 = 4cm
4. B: 6 x 4 = 24cm
5. Add them together: 24 + 4 = 28cm
2
Exam questions
Exam style questions
Solution
How to solve
1. Split the shape into a rectangle and triangle.
2. Triangle area: 7 x 6 = 42 ÷ 2 = 21m
3. Rectangle area: 14 x 18 = 252m
4. Add them together: 21 + 252 = 273m
5. Divide by chicken space! 273 ÷ 5 = 54.6
6. We can't have 0.6 of a chicken, so total is 54 chickens.
Next steps
Home learning task to be completed by next session
What's next?
Next time
We will look at volume of cubes and cuboids