Area & Perimeter of Composite Shapes explained through a friendly whiteboard conversation, examples, visuals, and practice for school students.
Step 1
Notes
Step 2
Formulae
Step 3
Examples
Step 4
Practice
Revise the definition, formulae, important results, and exam method first.
Use the sticky diagram while this dedicated tool is being prepared.
Solve only this concept and let the app adapt from your answers.
You have met the idea. Now open a tiny puzzle, a useful fact, and the next best action.
Continue the journey
A composite shape is made by joining two or more simple shapes.
To find its area or perimeter, break it into shapes you already know.
Composite shapes appear in floor plans, gardens, paths, tiles, and exam diagrams.
Composite shapes look difficult at first because they have more than one part.
The area can usually be found by splitting the shape into familiar parts and adding their areas.
Sometimes it is easier to place the shape inside a larger rectangle and subtract the missing part.
Perimeter is different from area. For perimeter, trace only the outside boundary. Do not include inside joining lines.
Meaning: Split a complex shape into simple shapes.
Definition: The splitting method finds total area by adding areas of noverlapping parts.
An hape can be split into two rectangles. Find both areas and add them.
Meaning: Subtract a missing part from a larger shape.
Definition: The subtracting method finds area by taking away unused area from a complete shape.
An hape can be seen as a large rectangle with a smaller rectangle removed.
Meaning: Composite perimeter is the distance around the outside.
Definition: Perimeter of a composite shape is the sum of all outer side lengths.
Inner dividing lines are not part of the outside boundary.
Meaning: Some side lengths are not directly given.
Definition: Missing lengths can often be found by comparing opposite total lengths.
If a full horizontal length is 12 cm and one part is 5 cm, the missing part may be 7 cm.
Easy
Question: A composite shape is made of two rectangles with areas 24 c and 15 c. Find total area.
Medium
Question: A large rectangle has area 80 c. A small rectangle of area 18 c is removed. Find the remaining area.
Exam-level
Question: An hape has outer sides 10 cm, 8 cm, 4 cm, 3 cm, 6 cm, and 5 cm. Find its perimeter.
Adding inner lines to perimeter
Why it happens: Every visible line is counted.
Correct approach: Trace only the outside boundary.
Doublounting overlapping area
Why it happens: Parts are not split cleanly.
Correct approach: Use noverlapping parts.
Using one formula for the whole shape
Why it happens: The shape is treated as a simple rectangle.
Correct approach: Break the shape into known simple shapes.
Should I split or subtract?
Use the method that makes the diagram easier. Both can be correct.
Do internal lines count in perimeter?
No. Perimeter is only the outside boundary.
Can a composite shape include curved parts?
Yes. Then circle formulas may be needed for the curved parts.
Practise the same concept from this article. Your student profile may guide entitlement and follop recommendations, but it does not replace this concept.