Arc length and area of a sector

When solving for $r$ or $\theta$, algebra slips are common; keep the $\dfrac{\theta}{360}$ fraction intact while rearranging.

Some find a triangle area or subtract values that the question did not ask for.

Arc length uses $2\pi r$; sector area uses $\pi r^2$. Both are multiplied by $\dfrac{\theta}{360}$, so the only difference is the circle formula inside. Using $\pi r^2$ for an arc, or $2\pi r$ for an area, is a common mix-up — check whether the answer is a length (cm) or an area (cm²).

The perimeter of a sector is the arc PLUS the two straight radii: $\text{arc} + 2r$. Giving only the arc length, or adding just one radius, is a frequent error. For radius $7$ and $90°$: arc $= 3.5\pi$, so perimeter $= 3.5\pi + 14 \approx 25.0$ cm.

Keep $\pi$ exact (or use the calculator value) through the working and round only the final answer to the accuracy asked. Rounding $\pi$ to $3.14$ mid-question, or rounding the area before the last step, can push the final digit out and cost the accuracy mark.