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Semicircle and quadrant areas

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

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Student-friendly explanation

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.

How to write this in exams

  1. 1

    Start with the exact idea

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

  2. 2

    Then show how to use it

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

  3. 3

    Add one concrete example

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

  4. 4

    Avoid this incomplete answer

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

Definition

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

Example

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

Rule to remember

Semicircle area = 1/2 × πr². Quadrant area = 1/4 × πr².

Memory hook

Half circle, quarter circle, same radius, smaller share.

Examples and method

Worked example

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

Method to apply

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

Diagram support

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

How CBSE asks it

Find the area of a semicircular or quarter-circular region, or compare them with full circles.

Avoid common mistakes

Common confusion

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

Common wrong answer

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

Exam tip

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

Quick check

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

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.

Answer writing and exam use

1-mark answer

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

2-mark answer

A semicircle is half of a circle, and a quadrant is one-fourth of a circle. Semicircle area = 1/2 × πr². Quadrant area = 1/4 × πr². If radius is 14 cm, area of semicircle = 1/2 × π × 14² = 98π cm².

3-mark answer

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. Semicircle area = 1/2 × πr². Quadrant area = 1/4 × πr². For r = 7 cm, semicircle area = 1/2 × 154 = 77 cm². Quadrant area = 1/4 × 154 = 38.5 cm². Find the area of a semicircular or quarter-circular region, or compare them with full circles. A common wrong answer is to use diameter 14 cm as radius and then halve the result again.
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