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### PERIMETER

**Definition**

**Example:**

#### Perimeter By Using A Formula

The perimeter of some polygons can be calculated directly by using a formula.

Let us calculate the perimeter of a rectangle and square by using a formula.

### PERIMETER OF A RECTANGLE

Therefore, perimeter = l + b + l + b = l + l + b + b = 2× l + 2 × b = 2 (l + b)

**Examples:**

1. Find the perimeter of a rectangle whose length is 5 cm and breadth is 4 cm.

**Solution:**

Here, length of the rectangle = 5 cm

Breadth of the rectangle = 4 cm

Perimeter of the rectangle = 2 (length + breadth)

= 2 (5 cm + 4 cm)

= 2 (9 cm)

= 18 cm.

Hence, the perimeter of the rectangle is 18 cm.

2. Find the length of the wire required to fence 3 rounds of a rectangular ground of length 20 m and breadth 15 m. Also find the cost of fencing the ground at the rate of ₨ 2 per metre.

Solution: Length of the ground = 20 m

Breadth of the ground = 15 m

Perimeter = 2 (length + Breadth)

= 2 (20 + 15)

= 2(35)

= 70m

Total wire required to fence 3 rounds of ground

= 3 × 70 m = 210 m

Cost of fencing 1m = ₨ 2

Cost of fencing 210 m = 210 × 2

Cost of fencing = ₨ 420

### PERIMETER OF A SQUARE

Therefore, Perimeter of a square = 4s = 4 × side

**Examples:**

1. Find the perimeter of a square whose side is 13 cm.

Solution:

Side of a square = 13 cm

Perimeter of a square = 4 × side

= 4 × 13 cm

= 52 cm.

2. Find the side of a square whose perimeter is 36 cm.

**Solution: ** Perimeter of the square = 36 cm

Perimeter = 4 × side

36 = 4 × side

Side = 36 ÷ 4

Side = 9 cm.

### PERIMETER OF A TRIANGLE

So, Perimeter of a triangle, P = a + b + c

Example: Find the perimeter of a triangle whose sides are 11 cm, 13 cm, and 8 cm

**Solution:**

Perimeter of a triangle = sum of its sides

= 11 + 13 + 8

= 32 cm

So, the perimeter of the triangle = 32 cm.