Perimeter and Area of Plane Figures
ICSE Class 6 · Mathematics · Chapter 32
What this chapter covers
- Perimeter: the distance around a shape
- Perimeter of a rectangle and a square
- Shapes with the same perimeter
- Area: the space a shape covers
- Area of a rectangle and a square
- Conversion of units
- Clearing up mix-ups about perimeter and area
Key definitions
Perimeter is the total length of the boundary of a closed plane figure.
Area is the amount of flat surface that a closed plane figure covers.
Capacity is the amount of liquid that a container can hold, such as the milk in a jug or the water in a bucket.
Key points
- Perimeter is the total length of the boundary of a closed figure; add the lengths of all its sides.
- Perimeter of a rectangle = 2 × (length + breadth); perimeter of a square = 4 × side.
- Different shapes, even very different ones, can have the same perimeter.
- Area is the amount of surface a closed figure covers, counted in unit squares.
- Area of a rectangle = length × breadth; area of a square = side × side.
- Perimeter is in units of length (cm, m); area is in square units (sq cm, sq m).
- To change a larger unit into a smaller one, multiply; to change a smaller unit into a larger one, divide.
- 1 kg = 1,000 g, 1 L = 1,000 mL, ₹1 = 100 paise, 1 h = 60 min, 1 min = 60 s, 1 day = 24 h.
- Same perimeter does not mean same area, and same area does not mean same perimeter.
Questions answered
What is the perimeter of a triangle with sides 9 cm, 12 cm and 15 cm?
9 + 12 + 15 = 36 cm.
Find the perimeter of a rectangle 14 m long and 9 m broad.
2 × (14 + 9) = 2 × 23 = 46 m.
A square handkerchief has a perimeter of 100 cm. What is the length of each side?
100 ÷ 4 = 25 cm.
Name two different rectangles, with whole-number sides, that each have a perimeter of 20 cm.
Any two pairs that add to 10 cm, for example 8 cm by 2 cm and 6 cm by 4 cm.
Find the area of a rectangular notice board 3 m long and 2 m broad.
3 × 2 = 6 sq m.
A square chessboard has a side of 40 cm. Find its area.
40 × 40 = 1,600 sq cm.
Convert: (a) 5 L into millilitres; (b) 420 min into hours; (c) ₹12 into paise.
(a) 5,000 mL; (b) 7 h; (c) 1,200 paise.
Painting a wall and fencing a park: which needs area and which needs perimeter?
Painting a wall needs area; fencing a park needs perimeter.