Quadrilaterals are the closed figures made of four straight line segments joined to each other at the vertex.
Look at the following quadrilateral, the length of each line segment is shown in the figure.
The sum of all its sides is
4 cm + 3 cm + 3 cm + 5 cm = 15 cm
Remember: The perimeter of a closed figure is the sum of lengths of all its sides.
The perimeter of a quadrilateral shown above is 15 cm.
Example 1:
Find the perimeter of the triangle ABC.
The perimeter of the triangle ABC is the sum of all its sides:
= AB + BC +AC
= 7cm + 5cm + 6cm
= 18cm
Perimeter of a rectangle
Example 2:
Find the perimeter of the rectangle PQRS.
The perimeter of the rectangle PQRS
= PQ + QR +RS + SP
= 4cm + 2cm + 4cm + 2cm
= 12cm
Since opposite sides of rectangles are equal in length. Hence the formula for finding the perimeter is
Perimeter of a rectangle = 2 ⨯ (length + breadth)
Perimeter of the rectangle PQRS can be found using the formula as follows:
= 2 ⨯ ( PQ + QR) cm
= 2 ⨯ (4 + 2) cm
= 2 ⨯ 6 cm
= 12cm
Perimeter of a square
Since the perimeter of a square is the sum of all its equal sides, we can say that the perimeter of a square is 4 times the side.
The perimeter of a square = 4 ⨯ side
Example 3:
Find the perimeter of square ABCD.
The perimeter of square ABCD
= 4 ⨯ 8 cm
= 32 cm
Exercise 8.1
A. Find the perimeter of the square whose sides are as follows:
| 1. 1 cm | 2. 3 cm | 3. 10 cm | 4. 15cm | 5. 30 cm | 6. 55 cm |
B. Find the perimeter of the rectangles whose length and breadth are as follows:
1. Length = 6 cm breadth = 3 cm
2. Length = 8 cm breadth = 4 cm
3. Length = 10 cm breadth = 6 cm
C. Find the perimeter of triangles whose sides are as follows:
1. 5 cm, 7 cm , 7 cm
2. 13 cm, 12 cm, 14 cm
3. 15 cm, 27 cm, 25 cm
Story Sums
Example 4:
Ananya has to decorate her rectangular class board by placing colourful tapes around its border.The length and breadth of the board is 75 cm and 30 cm, respectively.Find the length of tape that Ananya will need to stick around the board.
The length of tape that Neeta needs = perimeter of the board
The perimeter of board = 2 ⨯ (length + breadth)
= 2 ⨯ (45 + 20) cm
= 2 ⨯ & 65 cm
= 130 cm
Ananya needs 130 cm of tape.
Example 5:
Here is a layout of Shanaya's home garden.It has to be fenced all around.Find the length of the fence required.
Length of fence required = perimeter of the garden
Perimeter of the garden = 20 m + 10 m + 15 m + 25 m = 70 m
Length of fencing required = 165 m
Exercise 8.2
1. Ajay bought a square piece of cloth of length 25 cm. Find the perimeter of the cloth.
2. A rectangular park of length 70 m and breadth 20 m need to be paved.Find the number of metres that has to be paved.
3. Mr Bajaj walks around a square garden of side 1 km. how much distance does he cover in 2 rounds?
4. The perimeter of a square field is 100 m. find the length of its side.(Hint: Side of a square = perimeter ÷ 4)
5. Siya and Piya are preparing for the Annual school sports day. Siya runs three rounds around an equilateral triangle field with side 50 m. Piya runs two rounds around a square field of side 30 m. find who runs a longer distance and by how much.
6. The perimeter of a rectangular field is 68 m. If its length is 24 metre, find its breadth.