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Activities for Introducing Perimeter

The perimeter of a geometric figure is the distance around the exterior of the shape. Perimeter may be applied to polygons, circles and compound shapes. Polygons are a large grouping of closed shapes with straight sides, which includes squares, rectangles, triangles and trapezoids. There are formulas to help find the perimeters of some shapes but it often comes down to simply adding the lengths of the sides.

Regular Polygons
- In a regular polygon, all sides are equal in length. The class of regular polygons includes squares, equilateral triangles, quadrilaterals, pentagons and hexagons. Determining the perimeter for a regular polygon can be made easy by multiplying the number of sides and the length of a side. For example, a square with a side measuring 2 centimeters would have a perimeter of 4 * 2 = 8 since a square has four sides.
  
  Learn to work these problems backwards. For example, a problem may ask the length of each side for a pentagon with a perimeter of 20. Calculate the answer by dividing the number of sides from the perimeter: 20 / 5 = 4.
Irregular Polygons
- Irregular polygons have sides of differing lengths. But in rectangles and parallelograms, there are still sides that are equal to each other. Rectangles have a matching pair of long sides, called the length, connected by a matching pair of short sides, called the width. The formula for finding a rectangle's perimeter is 2l + 2w where the "l" is length and "w" is width.
  
  Parallelograms have two long straight sides that equal and two slanted, shorter sides that are equal. The formula for a parallelogram's perimeter is 2a + 2b, where "a" is the longer side and "b" is the slanted side.
  
  If an irregular polygon does not have sides that are equal, such as with a right triangle, you will simply need to manually add the value of all of the sides. For example, a right triangle with sides measuring 3 and 5 and a hypotenuse of 8 would have a perimeter of 3 + 5 + 8 = 16.
Circle
- The perimeter of a circle can be calculated using either the diameter or the radius. Diameter is the straight line interior distance from one side of the circle to the other. Radius is the interior distance from the center of the circle to the side, which is also half the diameter. The formulas for circle perimeter are πd or 2πr.
Compound Shapes
- Compound shapes are irregularly shaped geometric figures that often look as though two shapes, such as a rectangle and square, have been conjoined. If all of the sides are given, simply add the values for the perimeter. But if there are missing sides, you'll need to determine the unknown values.
  When solving an unknown value for a compound shape, rely upon the given information. For example, if the long straight bottom is equal to 20 and the upper boundary consists of a square that's 5 across with an unknown quantity beside it, simply subtract: 20 - 5 = 15 as the width of the unknown region.

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