Find the perimeter of polygons and the circumference of circles.
Free, timed SHSAT practice sets on perimeter & circumference— every question includes a full worked explanation, and there's no account required.
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Perimeter is the distance around a shape, so you add up the lengths of all the sides. A circle's perimeter is called its circumference.
Common traps: multiplying length by width (that gives the area, 21 for the 7 by 3 rectangle), adding \(l + w\) and forgetting to double, mixing up radius and diameter, and using \(\pi r^2\) (area) instead of \(2\pi r\). Check your units too: perimeter is a length, not square units.
Perimeter \(= 2(l + w) = 2(11 + 23) = 68\) m. (Multiplying \(11 \times 23\) gives the area, 253. Adding \(11 + 23\) and forgetting to double gives 34. Adding only three sides, \(11 + 11 + 23\), gives 45.)
Circumference \(= \pi d = \pi(22) = 22\pi\) m. (Using the radius 11 in place of the diameter gives \(11\pi\). Using \(2\pi r\) with the diameter 22 as \(r\) gives \(44\pi\). Using the area formula \(\pi r^2 = \pi(11)^2\) gives \(121\pi\).)
A regular nonagon has 9 equal sides, so perimeter \(= 9 \times 3 = 27\) yd. (Adding \(9 + 3\) instead of multiplying gives 12. Counting only 8 sides gives 24. Using \(n - 2 = 7\) from the angle-sum formula gives 21.)