Introduction
Perimeter is the total distance around the edge of a closed 2D shape. Imagine walking along the boundary of a park; the total distance you cover is the perimeter. It is calculated by adding the lengths of all the sides.
Visual representation of calculating the boundary distance for various shapes.
Explanation Step by Step
To find the perimeter, identify all the side lengths of the shape. Ensure all measurements are in the same unit. Add them up to get the final result.
Sub-topics
1. Perimeter of a Triangle
A triangle has 3 sides. Perimeter = Side 1 + Side 2 + Side 3.
Examples
Example 1: Real-life Scenario
Tricky Example
2. Perimeter of Quadrilaterals and Polygons
For any polygon, sum up all its exterior sides. For a regular polygon (where all sides are equal), Perimeter = Number of sides × Side length.
Tricks and Shortcuts
- For a Square, use: 4 × Side.
- For a Rectangle, use: 2 × (Length + Breadth).
Common Mistakes
- Do not add interior lines; only the boundary sides count.
- Always check if units are consistent (don't add meters to centimeters).
Practice Questions
Easy Questions
- Find the perimeter of a triangle with sides 6 cm, 8 cm, and 10 cm.
- What is the perimeter of a square with a side of 12 cm?
- Tricky Question: A shape has 4 sides of 5 cm each, but it is not a square. What is its perimeter?
Medium Questions
- A rectangular field is 25 m long and 15 m wide. Find the distance covered by a person walking around it once.
- Find the perimeter of a regular hexagon with each side measuring 7 cm.
- Real-life Tricky Question: A farmer wants to fence a square plot of side 30 m with two rows of wire. How much wire is needed?
Hard Questions
- The perimeter of a rectangle is 50 cm. If its length is 15 cm, find its width.
- A wire in the shape of an equilateral triangle of side 12 cm is bent into a square. What is the side of the square?
- Tricky Real-life Question: A pentagonal park has sides of 10 m, 12 m, 15 m, 10 m, and 8 m. If a runner runs 1000 m, how many full rounds of the park did they complete?
Revision Summary
Perimeter is the boundary length. Use addition for all sides. Remember specific formulas for regular shapes like squares and rectangles to save time.