Perimeter of Irregular Shapes
Regular shapes like rectangles and squares have simple formulas for perimeter. But many shapes in real life are not regular — they have sides of different lengths and angles that are not equal.
These are called irregular shapes. To find their perimeter, you simply add up the lengths of all the sides.
In Class 6, you will learn to find the perimeter of irregular polygons and shapes made by combining rectangles and squares.
What is Perimeter of Irregular Shapes - Grade 6 Maths (Mensuration)?
Definition: The perimeter of any shape is the total distance around it. It is the sum of all the side lengths.
Perimeter = Sum of all sides
For irregular shapes, there is no shortcut formula. You must know or measure every side and add them up.
Perimeter of Irregular Shapes Formula
Steps to find the perimeter of an irregular shape:
- Identify and label all the sides of the shape.
- If any sides are missing, use the given information to calculate them.
- Add up all the side lengths.
- Write the answer with the correct unit (cm, m, etc.).
Finding missing sides in L-shapes and T-shapes:
- In combined shapes (like an L-shape made of two rectangles), some sides may not be labelled.
- Use the fact that opposite sides of the full rectangle must add up correctly.
- Example: If the total height on the left is 10 cm and one part is 6 cm, the other part is 10 − 6 = 4 cm.
Types and Properties
Common irregular shapes:
- Irregular pentagon: 5 sides, all different lengths. Perimeter = sum of all 5 sides.
- Irregular hexagon: 6 sides, all different lengths. Perimeter = sum of all 6 sides.
- L-shape: Made by cutting a rectangle from a larger rectangle. Has 6 sides.
- T-shape: Made by combining two rectangles. Has 8 sides.
- Any curved shape: If the boundary has curves, measure or estimate the curved part separately.
Note: For shapes on a grid (square paper), you can count the number of unit edges along the boundary to find the perimeter.
Solved Examples
Example 1: Irregular Pentagon
Problem: An irregular pentagon has sides 5 cm, 7 cm, 4 cm, 6 cm, and 3 cm. Find its perimeter.
Solution:
Perimeter = 5 + 7 + 4 + 6 + 3 = 25 cm
Example 2: Irregular Quadrilateral
Problem: A field in the shape of an irregular quadrilateral has sides 120 m, 85 m, 95 m, and 110 m. Find the perimeter.
Solution:
Perimeter = 120 + 85 + 95 + 110 = 410 m
Example 3: L-Shaped Figure
Problem: An L-shaped room has the following measurements: outer length = 12 m, outer width = 8 m. The cut-out is 5 m long and 3 m wide. Find the perimeter.
Solution:
The L-shape has 6 sides:
- Bottom: 12 m
- Right side: 8 m
- Top (partial): 12 − 5 = 7 m
- Step down: 8 − 3 = 5 m
- Step across: 5 m
- Left side: 3 m
Perimeter = 12 + 8 + 7 + 5 + 5 + 3 = 40 m
Example 4: Irregular Hexagon
Problem: An irregular hexagon has sides 3 cm, 5 cm, 2 cm, 6 cm, 4 cm, and 3.5 cm. Find its perimeter.
Solution:
Perimeter = 3 + 5 + 2 + 6 + 4 + 3.5 = 23.5 cm
Example 5: Shape on a Grid
Problem: A shape on a square grid has its boundary running along 14 grid edges. Each grid edge is 1 cm. Find the perimeter.
Solution:
Perimeter = 14 × 1 cm = 14 cm
Example 6: Fencing an Irregular Plot
Problem: A garden has 5 sides measuring 15 m, 20 m, 18 m, 12 m, and 25 m. Find the total length of fencing needed.
Solution:
Fencing = Perimeter = 15 + 20 + 18 + 12 + 25 = 90 m
Example 7: Finding a Missing Side from Perimeter
Problem: A quadrilateral has perimeter 50 cm. Three sides are 11 cm, 14 cm, and 13 cm. Find the fourth side.
Solution:
Fourth side = 50 − (11 + 14 + 13) = 50 − 38 = 12 cm
Example 8: Combined Shape with Known Sides
Problem: Two rectangles are joined to make a T-shape. Rectangle 1 is 10 cm × 3 cm (horizontal top). Rectangle 2 is 4 cm × 8 cm (vertical stem). Find the perimeter of the T-shape.
Solution:
The T-shape has 8 outer sides:
- Top: 10 cm
- Right of top: 3 cm
- Step right: (10 − 4)/2 = 3 cm
- Right of stem: 8 cm
- Bottom of stem: 4 cm
- Left of stem: 8 cm
- Step left: 3 cm
- Left of top: 3 cm
Perimeter = 10 + 3 + 3 + 8 + 4 + 8 + 3 + 3 = 42 cm
Real-World Applications
Where perimeter of irregular shapes is used:
- Fencing a garden: Most gardens and plots are not perfect rectangles. You add all side lengths to find fencing needed.
- Skirting a room: L-shaped or T-shaped rooms need skirting around all walls.
- Borders for art: Putting a border around a shaped card or frame.
- Walking tracks: Jogging tracks around parks follow irregular paths.
- Maps: Measuring borders of states, districts, or countries.
Key Points to Remember
- The perimeter of any shape = sum of all side lengths.
- For irregular shapes, there is no shortcut formula — add up all the sides.
- For L-shapes and T-shapes, find the missing sides first using subtraction.
- On a grid, count the boundary edges to find the perimeter.
- If the perimeter is given and one side is unknown, subtract the known sides from the perimeter.
- Always write the correct unit (cm, m, km) with the answer.
Practice Problems
- An irregular triangle has sides 8 cm, 6.5 cm, and 10 cm. Find the perimeter.
- An L-shaped figure has outer dimensions 15 m × 10 m. The cut-out is 7 m × 4 m. Find the perimeter.
- A hexagonal plot has sides 22 m, 18 m, 25 m, 20 m, 15 m, and 30 m. How much fencing is needed?
- A shape on a grid paper has its boundary running along 20 unit edges. What is its perimeter?
- A quadrilateral has perimeter 64 cm. Three sides are 15 cm, 18 cm, and 12 cm. Find the fourth side.
- An irregular garden has 7 sides. The sides measure 10 m, 6 m, 8 m, 12 m, 5 m, 9 m, and 14 m. Find the perimeter.
Frequently Asked Questions
Q1. How do I find the perimeter of an irregular shape?
Add up the lengths of all the sides. There is no shortcut formula for irregular shapes.
Q2. What if some sides are not labelled?
Use the other given measurements to calculate the missing sides. For example, in an L-shape, subtract known parts from the full length or width.
Q3. Is the perimeter of an irregular shape always more than a regular shape?
Not necessarily. The perimeter depends on the actual side lengths, not on whether the shape is regular or irregular.
Q4. How do I find perimeter on a grid?
Count the number of edges (unit sides) along the boundary of the shape. Each edge equals one unit of length.
Q5. What is the difference between perimeter and area?
Perimeter is the total distance around the shape (measured in cm, m, etc.). Area is the space inside the shape (measured in cm², m², etc.).
Q6. Can I find the perimeter of a circle this way?
No, a circle has no straight sides. The distance around a circle is called the circumference and has its own formula (2πr). The add-all-sides method works only for polygons.
