C
CraftExam
medium difficulty5 min

Composite Figures

A composite figure is made by joining or removing two or more familiar shapes.

In one line: Break the figure, solve the pieces, then join the answers with correct signs.

Practice This Concept

Understand it

To find its area or perimeter, break the figure into known parts such as rectangles, triangles, semicircles, or sectors. Add areas for joined parts and subtract areas for cut-out parts.

Example

A rectangle of 20 cm by 10 cm has a semicircle of radius 5 cm removed. Required area = rectangle area - semicircle area.

Formula and rule

Composite area = sum of included parts - sum of removed parts.

Composite perimeter uses only the outer boundary or required boundary.

See it worked out

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

Worked example

  1. 1A 12 cm by 8 cm rectangle is joined to a right triangle with base 8 cm and height 6 cm.
  2. 2Total area = 12 × 8 + 1/2 × 8 × 6 = 96 + 24 = 120 cm².

Method you can reuse

Identify known shapes, decide whether each part is added or removed, calculate each area, combine carefully, and write the final unit.

Sketch it in your answer

Use light partition lines to split the figure into standard shapes and mark removed regions clearly.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

A square sheet has a circular hole cut from it. Should the circle's area be added or subtracted?

Think first, then show answer
The circle's area should be subtracted because the hole is removed from the square sheet.

Common wrong answer

Adding the area of a removed circular hole.

Why it loses marks: The shaded or material region becomes smaller.

Don't mix this up

Students add every visible number without deciding whether a part is added or removed.

Exam tip

Shade or mark the required region and write plus or minus signs before calculation.

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

Exams often give shaded regions, paths around parks, window designs, or figures made from rectangles and circles.
  1. 1

    Enough for 1 mark

    A composite figure is made by joining or removing two or more familiar shapes.

  2. 2

    Add for 2 marks

    Example: A rectangle of 20 cm by 10 cm has a semicircle of radius 5 cm removed. Required area = rectangle area - semicircle area.

  3. 3

    Add for 3 marks

    To find its area or perimeter, break the figure into known parts such as rectangles, triangles, semicircles, or sectors.

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