Coaching Centre
Perimeter and circumference
Perimeter of polygons and composite shapes, circumference of circles, and perimeter of semicircles, quadrants and sectors.
Circumference
A sector with angle $\theta$ has arc length $\dfrac{\theta}{360} \times 2\pi r$. Its perimeter is the arc plus two radii.
Find the perimeter of a quadrant (quarter circle) of radius $8$ cm, to 1 decimal place.
A running track is a rectangle $100$ m long with a semicircle of diameter $60$ m on each end. Find the length of one lap, to the nearest metre.
Find the perimeter of a quadrant of radius $8$ cm (1 d.p.).
$4\pi + 16$.
Find one lap of the track in Example 2 (nearest metre).
$60\pi + 200$.
Find the circumference of a circle with radius $4$ (2 d.p.).
$8\pi$.
Find the perimeter of a semicircle of radius $5$ (2 d.p.).
$5\pi + 10$.
The exact arc length of a $90^\circ$ sector with radius $6$ is:
$\tfrac{1}{4} \times 12\pi$.
A circle has circumference $10\pi$. Find its radius.
$2\pi r = 10\pi$.
Find the perimeter of a $60^\circ$ sector of radius $4$ (2 d.p.).
Arc $= \tfrac{60}{360} \times 8\pi \approx 4.19$. Add two radii: $4.19 + 8 = 12.19$.
A rectangle is $12$ by $8$. Find its perimeter.
$2(12 + 8)$.
New numbers every time. Keep going until you get five in a row.