🧱 See It
Area still means the same thing it always has: how much space is inside a shape. The trouble with a circle is that unit squares never tile it perfectly — there's always a curved edge slicing through the squares along the rim.
Here's why the formula works anyway: imagine cutting a circle into many thin pizza-slice wedges, then laying those wedges out side by side, alternating point-up and point-down. They rearrange into a shape that's approximately a parallelogram — with a height equal to the radius, and a length equal to half the circumference (since half the wedges point each way). That rearranged shape is where the area formula actually comes from — it isn't just a rule to memorize.
✏️ Draw It
The grid squares fill most of the circle, but the ones right at the curved rim get sliced off and don't count as whole squares — that's exactly why circles need their own formula instead of just counting.
🔢 Write It
Area = 3.14 × radius × radius
(also written A = πr²)
💡 Worked Examples
Example 1 — Circle with radius: 4 cm
- Formula:
A = 3.14 × radius × radius - Plug in:
A = 3.14 × 4 × 4 - Multiply the radii first:
A = 3.14 × 16 - Multiply:
A = 50.24 - Answer:
A = 50.24 cm²
Example 2 — Circle with radius: 7 cm
- Formula:
A = 3.14 × radius × radius - Plug in:
A = 3.14 × 7 × 7 - Multiply the radii first:
A = 3.14 × 49 - Multiply:
A = 153.86 - Answer:
A = 153.86 cm²
🧠 Quick Reference
| Circumference | Area | |
|---|---|---|
| Uses | diameter | radius |
| Squaring? | no | yes (radius × radius) |
| Answer units | cm (plain) | cm² (square) |