Introduction to Perimeter
Perimeter is the total length of the boundary of a closed figure. It is calculated by adding the lengths of all the sides of the shape. Understanding perimeter is essential for real-world tasks like fencing a garden or framing a picture.
Explanation Step by Step
To find the perimeter of any polygon, follow these steps:
Sub-topics
Geometry - Perimeter - Triangle, Rectangle, Square, Polygon
Different shapes have specific formulas to make calculations faster:
- Triangle: Sum of all 3 sides.
- Equilateral Triangle: 3 x side.
- Square: 4 x side.
- Rectangle: 2 x (Length + Width).
- Polygon: Sum of all exterior boundary lengths.
Examples
Example 1: Square
Tricks and Shortcuts
For regular polygons (where all sides are equal), simply multiply the length of one side by the total number of sides.
Common Mistakes
Do not forget to include the units (cm, m, km) in your final answer. Also, ensure all side lengths are in the same unit before adding them.
Practice Questions
Easy Questions
- Find the perimeter of a triangle with sides 3 cm, 4 cm, and 5 cm.
- A square has a side of 6 cm. What is its perimeter?
- Calculate the perimeter of a rectangle with length 10 cm and width 5 cm.
Medium Questions
- An equilateral triangle has a perimeter of 18 cm. Find the length of one side.
- A rectangular field is 15 meters long and 10 meters wide. How much wire is needed to fence it once?
- Find the perimeter of a pentagon where each side measures 7 cm.
Hard Questions
- The perimeter of a square is 40 cm. If this square is cut into two identical rectangles, what is the perimeter of one such rectangle?
- A wire of length 48 cm is bent to form a regular hexagon. What is the length of each side?
- A rectangular park has a perimeter of 100 m. If the length is 30 m, find the width and the cost of fencing it at 2 dollars per meter.
Revision Summary
Perimeter is the sum of all sides. Formulas: Square = 4s, Rectangle = 2(l+b), Triangle = a+b+c. Always check units before calculation.