To find the perimeter of a shape, you calculate the total length around its outer edge by adding together the lengths of all its sides.
General Method
- Add all side lengths: The perimeter is the sum of the lengths of every side of the polygon.
- For example, a triangle with sides 17 cm, 15 cm, and 11 cm has a perimeter of 17+15+11=4317+15+11=4317+15+11=43 cm
Specific Formulas for Common Shapes
Shape| Perimeter Formula| Explanation
---|---|---
Square| P=4×side lengthP=4\times \text{side length}P=4×side length| All four
sides are equal
Rectangle| P=2×(length+width)P=2\times
(\text{length}+\text{width})P=2×(length+width)| Sum of all four sides (2
lengths + 2 widths)
Triangle| P=a+b+cP=a+b+cP=a+b+c| Sum of the three side lengths
Circle| P=2πrP=2\pi rP=2πr| Circumference, where rrr is radius
- For a square with side length 6 cm, perimeter = 4×6=244\times 6=244×6=24 cm
- For a rectangle with length 7 and width 4, perimeter = 2×(7+4)=222\times (7+4)=222×(7+4)=22 units
- For a circle with radius rrr, perimeter (circumference) = 2πr2\pi r2πr
Steps to Find Perimeter
- Identify the shape and measure or note the length of each side.
- If the shape has equal sides (like a square), multiply the side length by the number of sides.
- If sides differ, add all side lengths together.
- Use the appropriate formula if the shape is standard (square, rectangle, triangle, circle).
- Ensure all side lengths are in the same units before adding.
- Write the answer with correct units.
Example
Find the perimeter of a rectangle with length 120 m and width 45 m:
P=2×(120+45)=2×165=330 mP=2\times (120+45)=2\times 165=330\text{ m}P=2×(120+45)=2×165=330 m
The perimeter is 330 meters
. In summary, the perimeter is the total distance around a shape, found by summing all side lengths or using specific formulas for regular shapes.
