Key ideas
- Area is the amount of space inside a shape. It is measured in squares: cm² or m².
- Perimeter is the distance all the way around the outside. It is a length: cm or m.
- For a rectangle, Area = length × breadth. For the perimeter, add all four sides.
- A composite shape is made from rectangles joined together. Split it up for area. For perimeter, find any missing sides first.
A = l × b
P = l + b + l + b
🌿 Every example on this page is set in the rainforest.
Counting squares
A scientist marks out a rectangular study plot on the rainforest floor. Her plan is drawn on centimetre squared paper. Find (a) the area and (b) the perimeter of the plot on the plan.(2 marks)
Count the squares inside.Area = 4 rows of 6 squares= 24 cm²✓1
In plain EnglishEach square is 1 cm by 1 cm, so each one is 1 cm². Count row by row: there are 4 rows of 6, which is 24 squares. Area is always in square units, so write cm².
Count the edges around the outside.Perimeter = 6 + 4 + 6 + 4= 20 cm✓2
In plain EnglishRun your finger around the outside and count each square edge you pass: 6 along the top, 4 down the side, 6 along the bottom and 4 back up. Perimeter is a length, so the units are cm, not cm².
⚠ Watch the units. Area is in cm² (squares). Perimeter is in cm (a length).
Using the formulae
A rectangular enclosure for poison dart frogs is 12 m long and 7 m wide. Calculate (a) the area and (b) the perimeter of the enclosure.(4 marks)
Write the formula and substitute.A = l × bA = 12 × 7✓1
In plain EnglishStart with the formula. Writing the formula doesn't get a mark on its own; putting the numbers in does. The length is 12 and the breadth is 7.
Work out the area.A = 84 m²✓2
In plain English12 × 7 = 84. The measurements are in metres, so the area is in square metres: m².
Add up all four sides.P = 12 + 7 + 12 + 7✓3
In plain EnglishA rectangle has two long sides and two short sides that match. So there are two 12s and two 7s to add.
Work out the perimeter.P = 38 m✓4
In plain English12 + 7 + 12 + 7 = 38. Perimeter is a length, so the units are m.
⚠ Common mistake. Adding just 12 + 7 = 19 only goes halfway round. Remember all four sides.
Composite area
A treetop viewing platform is the L-shape shown. Calculate its area.(4 marks)
Split the shape into two rectangles.Rectangle A: 4 m by 8 mRectangle B: (10 − 4) m by 3 m= 6 m by 3 m✓1
In plain EnglishDraw a line to cut the L into two rectangles, A and B. B's length isn't written on the diagram: the whole bottom is 10 m and A takes up 4 m of it, so B is 10 − 4 = 6 m long.
Find the area of each rectangle.Area A = 4 × 8 = 32 m²✓2Area B = 6 × 3 = 18 m²✓3
In plain EnglishUse length × breadth for each one.
Add the two areas together.Total = 32 + 18 = 50 m²✓4
In plain EnglishThe platform is made of both rectangles, so add the areas: 32 + 18 = 50 m².
⚠ Tip. You can split an L-shape either way. You'll get the same total area.
Composite perimeter
Scientists put a fence all the way around an L-shaped clearing to study jaguars. How much fencing do they need?(3 marks)
Find the first missing side.x = 9 − 5 = 4 m✓1
In plain EnglishSide x is part of the top edge. The top is 9 m and the bottom part is only 5 m, so the missing piece is 9 − 5 = 4 m.
Find the second missing side.y = 7 − 4 = 3 m✓2
In plain EnglishSide y is part of the left edge. The whole left side is 7 m and the right side takes up 4 m of that height, so y = 7 − 4 = 3 m.
Add all six sides.P = 9 + 4 + 4 + 3 + 5 + 7= 32 m✓3
In plain EnglishStart at one corner and go all the way round, so you don't miss a side. Tick each side off as you add it.
⚠ Common mistake. Only adding the sides with numbers on them. Find every missing side first.
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