Perimeter of Irregular Shapes
The perimeter of an irregular shape is found by adding up the lengths of all its sides. Unlike regular shapes (squares, rectangles) which have formulas, irregular shapes have sides of different lengths, so you must measure and add each one.
Irregular shapes appear often in real life — the boundary of a park, the outline of a state on a map, or the shape of a garden bed.
What is Perimeter of Irregular Shapes - Class 4 Maths (Measurement)?
Perimeter is the total distance around the boundary of a shape.
Perimeter of any shape = Sum of all side lengths
For regular shapes, shortcuts exist (e.g., square = 4 x side). For irregular shapes, there is no shortcut — you must add every side.
Solved Examples
Example 1: Example 1: Irregular Pentagon
Problem: Find the perimeter of a shape with sides 5 cm, 3 cm, 7 cm, 4 cm, and 6 cm.
Solution:
Perimeter = 5 + 3 + 7 + 4 + 6 = 25 cm
Answer: Perimeter = 25 cm
Example 2: Example 2: L-shaped Figure
Problem: An L-shaped room has sides: 8 m, 3 m, 5 m, 2 m, 3 m, 5 m. Find its perimeter.
Solution:
Perimeter = 8 + 3 + 5 + 2 + 3 + 5 = 26 m
Answer: Perimeter = 26 m
Example 3: Example 3: Finding a Missing Side
Problem: An irregular shape has sides 6 cm, 4 cm, 3 cm, ?, and 5 cm. Its perimeter is 23 cm. Find the missing side.
Solution:
Step 1: Sum of known sides = 6 + 4 + 3 + 5 = 18 cm
Step 2: Missing side = 23 − 18 = 5 cm
Answer: The missing side is 5 cm.
Example 4: Example 4: T-shaped Figure
Problem: A T-shaped garden has sides: 10 m, 3 m, 4 m, 7 m, 4 m, 3 m. Find its perimeter.
Solution:
Perimeter = 10 + 3 + 4 + 7 + 4 + 3 = 31 m
Answer: Perimeter = 31 m
Example 5: Example 5: Word Problem — Fencing
Problem: Arjun's garden is irregular with sides 12 m, 8 m, 15 m, 10 m, and 9 m. How much fencing wire does he need?
Solution:
Fencing = Perimeter = 12 + 8 + 15 + 10 + 9 = 54 m
Answer: Arjun needs 54 m of fencing wire.
Example 6: Example 6: Cross-shaped Figure
Problem: A plus (+) shaped figure has 12 sides, each 2 cm long. Find its perimeter.
Solution:
Perimeter = 12 x 2 = 24 cm
Answer: Perimeter = 24 cm
Example 7: Example 7: Composite Shape
Problem: A shape is made by joining a rectangle (8 cm x 4 cm) and a square (4 cm x 4 cm) along one side. Find the perimeter of the combined shape.
Solution:
Step 1: Draw the shape. The joined side (4 cm) is inside, not on the boundary.
Step 2: Outer sides: 8, 4, 4, 4, 4, 8 = wait, trace carefully.
Top: 8 cm. Right: 4 cm. Bottom-right: 4 cm. Bottom-step: 4 cm. Left-bottom: 4 cm. Left: 8 cm.
Perimeter = 8 + 4 + 4 + 4 + 4 + 8 = 32 cm... Let me trace more carefully:
Rectangle: 8 x 4, Square: 4 x 4 joined on a 4 cm side. Outer boundary: 8 + 4 + 4 + 4 + 4 + 8 = 32 cm. Subtract the 2 joined edges (4 + 4 = 8) but add back nothing... The perimeter of the composite = (2x8 + 2x4) + (4x4) − 2x4 = 24 + 16 − 8 = 32.
Actually: top = 8cm, right side of rect = 4cm, then step down, bottom of square = 4cm, left of square = 4cm, bottom of rect (8-4=4cm since square is attached), left of rect = 4+4=8cm. Total = 8+4+4+4+4+8 = 32 cm.
Answer: Perimeter = 32 cm
Example 8: Example 8: Using a String
Problem: Aditi uses a string to trace the boundary of an irregular shaped leaf. The string measures 28 cm. What is the perimeter?
Solution:
The length of the string equals the perimeter of the leaf.
Answer: Perimeter = 28 cm
Example 9: Example 9: Word Problem — Border
Problem: A notice board has an irregular shape with sides 40 cm, 25 cm, 35 cm, 20 cm, and 30 cm. A decorative border is placed around it. How long is the border?
Solution:
Border length = Perimeter = 40 + 25 + 35 + 20 + 30 = 150 cm
Answer: The border is 150 cm (or 1.5 m) long.
Key Points to Remember
- Perimeter = sum of all side lengths.
- For irregular shapes, measure and add every side — there is no shortcut formula.
- If one side is missing, subtract the sum of known sides from the total perimeter.
- For curved boundaries, use a string to measure the perimeter.
- Perimeter is measured in linear units (cm, m, km).
- Composite shapes: trace the outer boundary only — do not count shared internal sides.
Practice Problems
- Find the perimeter of a shape with sides 7 cm, 5 cm, 9 cm, 3 cm, and 6 cm.
- An L-shaped garden has sides 10 m, 4 m, 6 m, 3 m, 4 m, 7 m. Find its perimeter.
- A shape has a perimeter of 36 cm. Five of its six sides are 5, 8, 7, 4, and 6 cm. Find the sixth side.
- Dev traces around an irregular stone with a string. The string is 45 cm. What is the perimeter?
- A plus-shaped tile has 12 sides, each 3 cm. Find its perimeter.
- Neha's garden has sides 15 m, 12 m, 18 m, and 20 m. How much fencing does she need?
Frequently Asked Questions
Q1. How do you find the perimeter of an irregular shape?
Add the lengths of all the sides. There is no special formula — just measure every side and find the total.
Q2. What if one side length is unknown?
Subtract the sum of all known sides from the total perimeter. The result is the missing side length.
Q3. How do you measure the perimeter of a curved shape?
Use a string or thread. Place it along the boundary, then straighten and measure it with a ruler.
Q4. What is the difference between perimeter and area?
Perimeter is the distance around the boundary (in cm or m). Area is the surface enclosed (in sq cm or sq m).
Q5. Can two shapes have the same perimeter but different areas?
Yes. A long thin rectangle and a nearly-square rectangle can have the same perimeter but different areas.
Q6. What is a composite shape?
A shape made by combining two or more simple shapes (like rectangles or triangles). To find its perimeter, trace only the outer boundary.
Q7. Why do internal sides not count for perimeter?
Perimeter is the distance around the outside of a shape. Internal lines where two shapes are joined are not part of the outer boundary.
Q8. Is perimeter of irregular shapes in NCERT Class 4?
Yes, finding the perimeter of irregular shapes by adding side lengths is part of the CBSE/NCERT Class 4 Maths measurement curriculum.
Related Topics
- Perimeter (Grade 4)
- Area and Perimeter Word Problems (Grade 4)
- Introduction to Area
- Area of Rectangle (Grade 4)
- Area of Square (Grade 4)
- Converting Units of Length (Grade 4)
- Converting Units of Weight (Grade 4)
- Converting Units of Capacity (Grade 4)
- Area by Counting Squares
- Relationship Between Area and Perimeter
