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CraftExam
medium difficulty5 min

Shaded region problems

Shaded region problems ask for the area of the part that is marked or coloured inside a figure.

In one line: Shaded area = big part minus cut-out part.

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Understand it

In these questions, the shaded part may be a difference of shapes, a sector with a triangle removed, or a circle part inside another shape. The key is to find what is shaded and then use addition or subtraction correctly. These questions reward neat diagrams and careful reading.

Example

If a circle lies inside a square and only the outside part is shaded, the shaded area is square area minus circle area.

Formula and rule

Shaded area = area of outer figure - area of inner unshaded figure, or a suitable combination of circle-part formulas.

See it worked out

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

Worked example

If square area = 196 cm² and circle area = 154 cm², shaded area = 42 cm².

Method you can reuse

  1. 1Identify the outer figure.
  2. 2Identify the inner figure or removed part.
  3. 3Compute each required area.
  4. 4Subtract carefully.
  5. 5Check the units and final region.

Sketch it in your answer

Mark the shaded part lightly and the unshaded part clearly so the subtraction step is obvious.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

A circle is inside a square and the space outside the circle is shaded. What should be done first?

Think first, then show answer
First find the area of the square and the area of the circle separately. Then subtract the circle area from the square area to get the shaded part.

Common wrong answer

A common wrong answer is to add the inner and outer areas instead of subtracting the removed portion.

Don't mix this up

Students often calculate the larger outer shape and forget to subtract the unshaded inner part.

Exam tip

In shaded-region questions, first identify what is not shaded. That usually tells you what to subtract.

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 shaded area in a circle-inside-square, sector-minus-triangle, or overlapping-figure setup.
  1. 1

    Enough for 1 mark

    Shaded region problems ask for the area of the part that is marked or coloured inside a figure.

  2. 2

    Add for 2 marks

    Example: If a circle lies inside a square and only the outside part is shaded, the shaded area is square area minus circle area.

  3. 3

    Add for 3 marks

    The key is to find what is shaded and then use addition or subtraction correctly.

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