Functional Skills Level 2 — Shape: Perimeter and Area

Area of Circles

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Real-World Applications

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The Area Formula

The area of a circle is the amount of space it covers. We use the formula:

A = π × r²  (read as "pi times r squared")
r = radius  |  If given the diameter: r = d ÷ 2 first
π ≈ 3.14159… Use the π button on your calculator for the most accurate answer. Your answer will be in square units (cm², m², etc.).
r = radius d = diameter = 2r Circle: radius, diameter A = π × r²
What Does "r Squared" Mean?

r² means r × r. For r = 5 cm, r² = 5 × 5 = 25 cm². Then we multiply by π (about 3.14159) to get the circle's area.

r = 5 cm = π × 5 cm 5 cm r² = 25 cm² Step 1 Square the radius: r² = 5 × 5 = 25 Step 2 Multiply by π: A = π × 25 Step 3 Answer: A ≈ 78.54 cm² A = π × r² = π × 25 ≈ 78.54 cm²
Worked Examples
Circle r = 7 cm Step 1 r² = 7² = 49 square the radius Step 2 A = π × 49 ≈ 153.94 cm² multiply by π

Example 1: Find the area of a circle with radius 5 cm.

Step 1
\(A = \pi \times 5^2 = 25\pi \approx \mathbf{78.54\text{ cm}^2}\)

Example 2: A circle has diameter 14 m. Find its area.

Step 1
Radius: \(r = 14 \div 2 = 7\text{ m}\)
Step 2
\(A = \pi \times 7^2 = 49\pi \approx \mathbf{153.94\text{ m}^2}\)
Always halve the diameter to get the radius before using the formula. A very common mistake is to use the diameter in A = πr² — this gives an answer 4 times too large!
✓ Quick Check 1 — Radius, Diameter and \(A = \pi r^2\)
Question 1 of 10
Finding the Radius from the Area

If you are given the area and need to find the radius, reverse the formula step by step.

r² = A ÷ π    then    r = √(A ÷ π)
Area given A = 50.27 cm² ÷ π r² = 50.27 ÷ π r² = 16 √ (square root) r = √16 r = 4 cm

Example 3: A circle has area 50.27 cm². Find its radius.

Step 1
\(r^2 = A \div \pi = 50.27 \div \pi \approx 16\)
Step 2
\(r = \sqrt{16} = \mathbf{4\text{ cm}}\)
Semicircles and Quarter Circles
Semicircle: A = πr² ÷ 2   |   Quarter circle: A = πr² ÷ 4

Example 4: Find the area of a semicircle with diameter 10 cm.

Step 1
Radius: \(r = 5\text{ cm}\)
Step 2
\(A = \dfrac{\pi \times 5^2}{2} = \dfrac{25\pi}{2} \approx \mathbf{39.27\text{ cm}^2}\)
For a semicircle, halve the full circle area. For a quarter circle, divide by 4.
✓ Quick Check 2 — Area from Diameter
Question 1 of 10
Circle Calculator

Circle Calculator

✓ Quick Check 3 — Real Life and Comparing Areas
Question 1 of 10

Practice: Area of Circles

Use A = π × r² (π ≈ 3.14159). Give answers to 2 decimal places, then click Check.

#QuestionAnswerResult
1Area of circle, r = 3 cm (cm²)
2Area of circle, r = 6 cm (cm²)
3Area of circle, diameter = 10 m (m²)
4Area of circle, r = 10 cm (cm²)
5Semicircle area, r = 4 cm (cm²)
6Area of circle, diameter = 6 m (m²)
7Find the radius if Area = 78.54 cm² (cm)
8Quarter circle area, r = 8 cm (cm²)
9Area of circle, r = 12 cm (cm²)
10A circular table has diameter 2.8 m. Find its area (m²)

⚠ Things to Watch Out For

  • The formula is πr² — if you're given a diameter, halve it to get the radius before squaring.
  • Square the radius, not π — it's π × r², not (π × r)².
  • Don't confuse the area formula (πr²) with the circumference formula (2πr or πd).
  • Never approximate π as 3 — use the π button on your calculator or leave the answer in terms of π.
  • If you forget to square the radius, you'll get the circumference formula instead of the area.
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