medium difficulty5 min

Combined figures involving circles

Combined figures involving circles are shapes made by joining a circle part with other geometric shapes such as rectangles, triangles, or semicircles.

In one line: Split, solve, and join again.

Practice This Concept

Understand it

These questions require careful separation of each part. Students must identify which area or boundary belongs to each shape, then add or subtract correctly. The answer depends on breaking the figure into smaller known parts.

Example

A rectangle with a semicircle on one side may need rectangle area plus semicircle area to get the total.

Formula and rule

Use the separate formulas for each part, then add or subtract as the figure demands.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

If a rectangle area is 48 cm² and the attached semicircle area is 14 cm², the total area is 62 cm².

Method you can reuse

1Break the figure into known shapes.
2Decide whether to add or subtract each part.
3Use the correct formula for every part.
4Keep units consistent.
5Write the final combined result.

Visual tip

Redraw the combined figure with labels for each sub-shape and mark any shared edges clearly.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

A shape has a rectangle and a semicircle attached together. What is the safest way to find its area?

Think first, then show answer

Find the area of each part separately and then add them if both parts are included. If any part is missing or cut out, subtract that part carefully.

Common wrong answer

A common wrong answer is to add all visible parts without checking whether some areas overlap.

Don't mix this up

Students often count the same region twice or forget to remove a part that is cut out.

Exam tip

Draw the figure again and label each part before starting calculation. A neat split reduces errors.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Find the area or perimeter of a figure made from circle parts and straight-edged shapes.

1
Enough for 1 mark
Combined figures involving circles are shapes made by joining a circle part with other geometric shapes such as rectangles, triangles, or semicircles.
2
Add for 2 marks
Example: A rectangle with a semicircle on one side may need rectangle area plus semicircle area to get the total.
3
Add for 3 marks
The answer depends on breaking the figure into smaller known parts.

MCQ Quiz

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