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medium difficulty5 min

Semicircle and quadrant areas

A semicircle is half of a circle, and a quadrant is one-fourth of a circle.

In one line: Half circle, quarter circle, same radius, smaller share.

Practice This Concept

Understand it

These are fractional parts of a full circle, so their areas are based on the area of the whole circle. Semicircle means divide by 2, and quadrant means divide by 4. Students should also remember that the diameter of a semicircle is twice the radius.

Example

If radius is 14 cm, area of semicircle = 1/2 × π × 14² = 98π cm².

Formula and rule

Semicircle area = 1/2 × πr².

Quadrant area = 1/4 × πr².

See it worked out

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

Worked example

  1. 1For r = 7 cm, semicircle area = 1/2 × 154 = 77 cm².
  2. 2Quadrant area = 1/4 × 154 = 38.5 cm².

Method you can reuse

  1. 1Identify whether the part is a semicircle or a quadrant.
  2. 2Use the full circle area formula first.
  3. 3Multiply by 1/2 or 1/4.
  4. 4Use the radius correctly.
  5. 5Write the answer in square units.

Sketch it in your answer

Draw a circle and show a diameter for a semicircle or two perpendicular radii for a quadrant.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

A circle is divided into 4 equal parts. What is the area of one part called?

Think first, then show answer
One part is called a quadrant, and it is one-fourth of the area of the whole circle. So you first find the full circle area and then divide by 4.

Common wrong answer

A common wrong answer is to use diameter 14 cm as radius and then halve the result again.

Don't mix this up

Students often use the diameter as if it were the radius, or forget the fraction factor 1/2 or 1/4.

Exam tip

For semicircle and quadrant questions, first find the area of the full circle, then take the correct fraction.

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 of a semicircular or quarter-circular region, or compare them with full circles.
  1. 1

    Enough for 1 mark

    A semicircle is half of a circle, and a quadrant is one-fourth of a circle.

  2. 2

    Add for 2 marks

    Example: If radius is 14 cm, area of semicircle = 1/2 × π × 14² = 98π cm².

  3. 3

    Add for 3 marks

    These are fractional parts of a full circle, so their areas are based on the area of the whole circle.

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