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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.

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Student-friendly explanation

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.

How to write this in exams

  1. 1

    Start with the exact idea

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

  2. 2

    Then show how to use it

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

  3. 3

    Add one concrete example

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

  4. 4

    Avoid this incomplete answer

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

Definition

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

Example

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

Rule to remember

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

Memory hook

Split, solve, and join again.

Examples and method

Worked example

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

Method to apply

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

Diagram support

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

How CBSE asks it

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

Avoid common mistakes

Common confusion

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

Common wrong answer

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

Exam tip

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

Quick check

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

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.

Answer writing and exam use

1-mark answer

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

2-mark answer

Combined figures involving circles are shapes made by joining a circle part with other geometric shapes such as rectangles, triangles, or semicircles. Use the separate formulas for each part, then add or subtract as the figure demands. A rectangle with a semicircle on one side may need rectangle area plus semicircle area to get the total.

3-mark answer

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. Use the separate formulas for each part, then add or subtract as the figure demands. If a rectangle area is 48 cm² and the attached semicircle area is 14 cm², the total area is 62 cm². Find the area or perimeter of a figure made from circle parts and straight-edged shapes. A common wrong answer is to add all visible parts without checking whether some areas overlap.
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