Concept 2 of 4
Area
Today's big idea
Area counts the unit squares inside, so a rectangle gives A = length × width.
To find the area of an odd shape, split it into rectangles and add the pieces.
How it works
👀 What's going on?
Perimeter told you how far it is round the edge. Area asks something different: how much flat space sits inside. You count that space in squares, not in centimetres.
💡 Here's the trick
Look at the grid above. The rectangle holds 5 rows of 8 unit squares, so you can multiply 8 × 5 instead of counting them one by one. Area is always a count of squares, which is why its unit is squared.
🪄 How to do it
- 1.Read the two side lengths off the grid above.
- 2.Multiply them to get the area of a rectangle.
- 3.Halve that product when the shape is a triangle.
✍️ Try it
What is the area of a rectangle 14 cm by 9 cm? Then: what is the area of a triangle with base 18 cm and height 6 cm?
The rectangle gives 14 × 9 = 126 cm². The triangle gives ½ × 18 × 6 = 54 cm².
⚠️ Watch out
You might be thinking a bigger perimeter always means a bigger area. A strip 1 cm by 8 cm has perimeter 18 cm and area 8 cm². A card 3 cm by 4 cm has a shorter perimeter of 14 cm, yet holds 12 cm².
🌟 Why this matters
Carpet, paint, floor tiles and lawn seed are all sold by area, so a shopkeeper needs length times width. Order by perimeter instead and half the room stays bare.
Exam tip: Check the unit printed in the options, because cm and cm² are the quickest way a paper catches you out.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“A square has side 7 cm. What is the AREA?”
- 1
Recall the formula
Square area = side × side. 🟦
- 2
Substitute
A = 7 × 7
- 3
Compute
7 × 7 = 49.
- 4
Re-state with units ✓
Area = 49 cm².
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Tap each square to lay a tile. Fill the whole shape to see the area.
RECTANGLE · ROUND 1 OF 3
3 rows × 4 cols · each tile 1 cm²
Tiles laid: 0 of 12 cm²
Quick check
✅ VERIFICATION
A right triangle has base 16 cm and height 7 cm. What is its AREA?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Volume
L × W × H · 1 L = 1,000 cm³.