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Shaded region problems

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

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Student-friendly explanation

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.

How to write this in exams

  1. 1

    Start with the exact idea

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

  2. 2

    Then show how to use it

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

  3. 3

    Add one concrete example

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

  4. 4

    Avoid this incomplete answer

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

Definition

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

Example

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

Rule to remember

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

Memory hook

Shaded area = big part minus cut-out part.

Examples and method

Worked example

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

Method to apply

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

Diagram support

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

How CBSE asks it

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

Avoid common mistakes

Common confusion

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

Common wrong answer

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

Exam tip

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

Quick check

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

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.

Answer writing and exam use

1-mark answer

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

2-mark answer

Shaded region problems ask for the area of the part that is marked or coloured inside a figure. Shaded area = area of outer figure - area of inner unshaded figure, or a suitable combination of circle-part formulas. If a circle lies inside a square and only the outside part is shaded, the shaded area is square area minus circle area.

3-mark answer

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. Shaded area = area of outer figure - area of inner unshaded figure, or a suitable combination of circle-part formulas. If square area = 196 cm² and circle area = 154 cm², shaded area = 42 cm². Find shaded area in a circle-inside-square, sector-minus-triangle, or overlapping-figure setup. A common wrong answer is to add the inner and outer areas instead of subtracting the removed portion.
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