How to find the area of a circle

• $r$ is the radius: the distance from the centre to the edge.
• The diameter $d$ goes all the way across through the centre, so $d = 2r$.
• $\pi \approx 3.14159$. Use the $\pi$ button on your calculator unless the question says otherwise.
• Area is measured in square units: mm², cm², m² or km².

$36\pi$ cm² is the exact answer. $113.10$ cm² is the answer rounded to 2 decimal places. Square the radius before you multiply by $\pi$.

Always halve the diameter first. Using $10$ instead of $5$ gives an answer four times too big.

A semicircle is half a circle and a quarter circle (a quadrant) is a quarter, so take that fraction of $\pi r^2$.

For composite shapes, split the shape into a rectangle, triangle or other shape plus the circle parts, find each area, then add (or subtract the cut-out).

A sector is a "pizza slice" of a circle, between two radii. If the angle at the centre is $\theta$ degrees, the sector is $\dfrac{\theta}{360}$ of the whole circle.

A semicircle is a sector with $\theta = 180^\circ$, and a quarter circle has $\theta = 90^\circ$.

Work backwards: divide by $\pi$, then take the square root.

Keep the full value of $\dfrac{50}{\pi}$ in your calculator before taking the square root, and round only at the end. Double it to get the diameter: about $7.98$ cm.

• Using the diameter instead of the radius. Halve the diameter first.
• Doubling instead of squaring. $r^2$ means $r \times r$, not $2 \times r$. For $r = 6$, $r^2 = 36$, not $12$.
• Squaring $\pi$ as well. $\pi r^2$ means $\pi \times r^2$. Only the radius is squared.
• Mixing up area and circumference. Area is $\pi r^2$ (square units). Circumference is $2\pi r$ (plain units).
• Rounding too early. Keep the full value until the last step.