Perimeter and Area Class 6 ICSE — Chapter 23
Perimeter and area class 6 ICSE maths begins in Chapter 23 of your textbook. This chapter teaches you to measure closed plane figures. You will define perimeter and area, apply both to squares and rectangles, convert units, and solve cost problems. This page explains each section in the book’s own order, with the formulas and worked patterns you need. Read alongside your book to follow every step.
Download Perimeter and Area of Plane Figures Class 6 ICSE Mathematics Chapter 23 PDF
Download the Perimeter and Area of Plane Figures Class 6 ICSE Mathematics chapter PDF to revise offline or print for practice. It is the full chapter as printed in the book — 8 pages, 3 sections, 36 questions.
What is inside Chapter 23
8 pages · 3 sections · 18 worked examples · 36 exercise questions
| Section | Title |
|---|---|
| 23.1 | INTRODUCTION |
| 23.2 | SOME DEFINITIONS |
| 23.3 | SOME IMPORTANT PLANE FIGURES |
- EXERCISE 23(A): 15 questions
- EXERCISE 23(B): 21 questions
23.1 INTRODUCTION
Mensuration is the branch of measurement that deals with length, area, volume and surface area. You already use it without noticing. Cloth for shirts is bought by length. A plot of land is bought by area. Milk and petrol are bought by volume.
This chapter narrows mensuration down to two ideas: perimeter and area. You will measure the boundary of a figure and the surface it encloses. Start with the Class 6 ICSE Maths chapters to see where this topic sits among the others. The official CISCE website lists the full syllabus for the year.
23.2 SOME DEFINITIONS
Perimeter is the length of the boundary of a closed figure. For a triangle, add its three sides. For a quadrilateral, add all four sides. The unit of perimeter is the same as the unit of length, such as centimetre (cm) or metre (m).
Area is the measure of the size of the surface enclosed by the boundary of a plane figure. If each side is measured in centimetres, the area is in square-centimetres (cm²). If each side is in metres, the area is in square-metres (m²).
Unit conversions matter before you add lengths. The chapter gives these facts:
- 1\ \text{m} = 100\ \text{cm}
- 1\ \text{m}^2 = 100 \times 100\ \text{cm}^2 = 10{,}000\ \text{cm}^2
- 1\ \text{cm} = \frac{1}{100}\ \text{m}
- 1\ \text{cm}^2 = \frac{1}{10{,}000}\ \text{m}^2
The common mistake is adding lengths in different units. Convert every side to the same unit first. For example, a triangle has sides of 50 cm, 2 m and 75 cm. In centimetres: 50 + 200 + 75 = 325\ \text{cm}. In metres: 0.5 + 2 + 0.75 = 3.25\ \text{m}. Both answers are correct because the units match.
23.3 SOME IMPORTANT PLANE FIGURES
A square is a four-sided closed figure with all sides equal and each angle 90°. Let each side be a. Its perimeter is P = 4a = 4 \times \text{side}. Its area is A = a^2 = (\text{side})^2.
You can reverse these formulas. When the perimeter is known, each side is \frac{P}{4}. When the area is known, each side is \sqrt{A}. These reverse forms appear in Class 6 ICSE Maths exercise questions.
Worked pattern: a square field has side 15 m. Its perimeter is 4 \times 15 = 60\ \text{m}. Its area is 15^2 = 225\ \text{m}^2. Fencing cost uses perimeter: at ₹20 per metre, 60 \times 20 = ₹1{,}200. Ploughing cost uses area: at ₹2 per m², 225 \times 2 = ₹450.
A rectangle is a four-sided closed figure with opposite sides equal and each angle 90°. Let length be l and breadth be b. Its perimeter is P = 2(l + b). Its area is A = l \times b.
Reverse forms: l = \frac{P}{2} - b, b = \frac{P}{2} - l, l = \frac{A}{b}, and b = \frac{A}{l}. Worked pattern: a rectangle has perimeter 40 cm and length 12 cm. Its breadth is \frac{40}{2} - 12 = 8\ \text{cm}. Its area is 12 \times 8 = 96\ \text{cm}^2.
Here is how the two figures compare at a glance.
| Quantity | Square (side a) | Rectangle (length l, breadth b) |
|---|---|---|
| Definition | All sides equal, each angle 90° | Opposite sides equal, each angle 90° |
| Perimeter | P = 4a | P = 2(l + b) |
| Area | A = a^2 | A = l \times b |
| Find a side | a = \frac{P}{4} or a = \sqrt{A} | l = \frac{P}{2} - b, l = \frac{A}{b} |
Equal areas do not mean equal perimeters. A square of side 18 m has area 324\ \text{m}^2. A rectangle with the same area and width 12 m has length \frac{324}{12} = 27\ \text{m}. Its perimeter is 2(27 + 12) = 78\ \text{m}, while the square’s perimeter is only 72 m.
For shaded regions, subtract the inner figure from the outer one. An outer square of side 10 cm has area 100\ \text{cm}^2. An inner square of side 4 cm has area 16\ \text{cm}^2. The shaded part is 100 - 16 = 84\ \text{cm}^2.
What to practise from Perimeter and Area Class 6 ICSE
Two exercise blocks close this chapter. Practise both in order.
- EXERCISE 23(A) — 15 questions
- EXERCISE 23(B) — 21 questions
Both blocks cover perimeter of triangles and squares, area and side of squares, rectangle length-breadth-perimeter-area problems, fencing and levelling costs, and square-versus-rectangle comparisons. When you finish, move on to Chapter 24 on Solids in the same book.
Perimeter and Area Class 6 ICSE frequently asked questions
How do I convert metres to centimetres when finding the perimeter of a triangle?
Multiply each metre value by 100. Then add all sides in centimetres. If a side is 2 m, write it as 200 cm before adding.
When do I use perimeter and when do I use area in fencing and ploughing problems?
Fencing runs along the boundary, so use perimeter. Ploughing or levelling covers the surface, so use area. Fencing cost is rate × perimeter; ploughing cost is rate × area.
How do I find the side of a square when only its area is given?
Take the square root of the area. If the area is 225\ \text{m}^2, the side is \sqrt{225} = 15\ \text{m}.
Why do a square and a rectangle with the same area have different perimeters?
Area and perimeter measure different things. A rectangle with a long, thin shape stretches its boundary even when its area matches a square’s. So the perimeters differ.
What is the difference between perimeter and area in Class 6 ICSE Maths?
Perimeter is the length of the boundary of a closed figure, measured in cm or m. Area is the measure of the surface enclosed by that boundary, measured in cm² or m².
Reference: ICSE Class 6 Mathematics textbook material, chapter 23: Perimeter and Area of Plane Figures — CISCE-aligned.