Perimeter of a Rectangle

We will discuss here how to find the perimeter of a rectangle. We know perimeter of a rectangle is the total length (distance) of the boundary of a rectangle.

In a rectangle we know that two opposite sides are equal. So, PQ = SR and PS = QR

If PS = l and PQ = b

$Perimeter of a Rectangle$

Perimeter of the rectangle = PQ + QR + RS + SP

= b +l + b + l

= 2b +2l

Again,

ABCD is a rectangle. We know that the opposite sides of a rectangle are equal.

$Perimeter of a Rectangle$

AB = CD = 5 cm and BC = AD = 3 cm

So, the perimeter of the rectangle ABCD = AB + BC + CD + AD = 5 cm + 3 cm + 5 cm + 3 cm = 16 cm

It can be written as 5 cm + 5 cm + 3 cm + 3 cm

= (2 × 5) cm + (2 × 3) cm

= 2 (5 + 3) cm

= 2 × 8 cm

= 16 cm

We add length and breadth twice to find the perimeter of a rectangle.

Perimeter of a rectangle = 2 (length + breadth)

A rectangle is a four sided figure in which

● Opposite sides are equal in length.

● Longer side is called length and shorter side is called breadth.

● All angles are equal to 90° (right angle).

$Perimeter of a Rectangle$

In the above figure ABCD is a rectangle.

Three children found the perimeter of this rectangle in three different methods.

1^st method:

Perimeter = 6 cm + 4 cm + 6 cm + 4 cm = 20 cm

2^nd method:

Perimeter = (2 6 cm) + (2 4 cm) = 12 cm + 8 cm = 20 cm

3^rd method:

Perimeter = 2 (6 cm + 4 cm) = 2 cm × 10 cm = 20 cm

All the three methods gave them the same answer.

Perimeter of a rectangle = length + breadth + length + breadth

= (2 length) + (2 breadth)

= 2 (length + breadth)

Word Problems on Perimeter of a Rectangle:

Let us consider some of the examples on perimeter of a rectangle:

1. The length of a rectangle is 4 cm and its breadth is 2 cm. Find its perimeter.

Solution:

Length = 4 cm

Breadth = 2 cm

$Examples on Perimeter of a Rectangle$

Therefore, perimeter of the rectangle

= 2 (length + breadth)

= 2 (4 + 2) cm

= 2 × 6 cm

= 12 cm

2. Find the perimeter of the rectangle ABCD whose sides are 6 cm and 5 cm.

Solution:

$Perimeter of Rectangle$

The perimeter of the rectangle ABCD

= 6 cm + 5 cm + 6 cm + 5cm

= 22 cm

3. Find the perimeter of a rectangle whose length is 12 cm and breadth is 8 cm.

Solution:

Length = 12 cm

Breadth = 8 cm

Perimeter = 2 (length + breadth)

= 2 (12 cm + 8 cm)

= 2 × 20 cm

= 40 cm

4. A rectangular swimming pool is 9 m long and 4 m broad. Find the area of the swimming pool.

Solution:

Length of the rectangular swimming pool = 9 m

Breadth of the rectangular swimming pool = 4 m

Therefore, perimeter of the rectangle swimming pool

= 2 (length + breadth)

= 2 (9 + 4) m

= 2 (13) m

= 2 × 13 m

= 26 m

5. The length of a rectangle is 4.5 m and the breadth is 1.5 m. Find the perimeter.

Solution:

Length = 4.5 m

Breadth = 1.5 m

$Perimeter of a Rectangle Problems$

Perimeter = 2 (length + breadth)

= 2 × (4.5 m + 1.5 m)

= 2 × 6 m

= 12 m

Therefore, the perimeter is 12 m.

6. A rectangle display board is measuring 8 m by 6 m. Robert wants to add a ribbon border around the display board. What is the length of ribbon that he will need? If the cost of the ribbon is $ 15 per metre then how much money does Robert needs to buy the ribbon?

Solution:

Length of the display board = 8 m

Breadth of the display board = 6 m

Perimeter of the display board = 2(Length + Breadth)

= 2(8 + 6) m

= 2 × 14 m

= 28 m.

Cost of ribbon is $15 per metre.

Therefore, total cost for 28 m long ribbon = $15 × 28

= $420.

Questions and Answers on Perimeter of a Rectangle:

1. Find the perimeter of the rectangles having measurements as follows.

(i) length = 11 cm breadth = 9 cm

(ii) length = 5 cm breadth = 2 cm

(iii) length = 10 cm breadth = 8 cm

(iv) length = 15 cm breadth = 2 cm

Answer:

1. (i) 40 cm

(ii) 14 cm

(iii) 36 cm

(iv) 34 cm

Perimeter of a Rectangle Word Problems

2. A rectangle has a perimeter of 40 cm. If its length is 8 cm, what is its breath?

Answer:

2. 12 cm

3. Sam is running around a rectangular park of length 450 m and breadth 300 m. Find the total distance covered by him if he takes 10 rounds of the park.

Answer:

3. 15000 m

4. A gardener wants to fence its rectangular garden with a wire. The length and breadth of the garden is 25 m and 16 m respectively. Find the length of the wire he must buy.

Answer:

4. 82 m

You might like these

Area | Units to find Area | Conversion Table of Area | Two Dimensional
The amount of surface that a plane figure covers is called its area. It’s unit is square centimeters or square meters etc. A rectangle, a square, a triangle and a circle are all examples of closed plane figures. In the following figures, the shaded region of each of the
Area and Perimeter |Units of Area| Formula of Area and Perimeter
Here we will learn about how to find area and perimeter of a plane figures. The perimeter is used to measure the boundaries and the area is used to measure the regions enclosed.
Perimeter of a Triangle | Perimeter of a Triangle Formula | Examples
We will discuss here how to find the perimeter of a triangle. We know perimeter of a triangle is the total length (distance) of the boundary of a triangle. Perimeter of a triangle is the sum of lengths of its three sides. The perimeter of a triangle ABC Perimeter
Perimeter of a Square | How to Find the Perimeter of Square? |Examples
We will discuss here how to find the perimeter of a square. Perimeter of a square is the total length (distance) of the boundary of a square. We know that all the sides of a square are equal. Perimeter of a Square Perimeter of the square ABCD = AB+BC+CD+AD=2 cm+2cm+2cm+2cm
Perimeter of a Figure | Perimeter of a Simple Closed Figure | Examples
Perimeter of a figure is explained here. Perimeter is the total length of the boundary of a closed figure. The perimeter of a simple closed figure is the sum of the measures of line-segments which have surrounded the figure.
Worksheet on Area and Perimeter of Triangle |Area & Perimeter| Answers
Practice the questions given in the worksheet on area and perimeter of triangle. Students can recall the topic and practice the questions to get more ideas on how to find the area of triangle and also the perimeter of triangle. 1. Find the area of a triangle having
Worksheet on Area and Perimeter | Word Problems | Answers
In worksheet on area and perimeter worksheet we will find the perimeter of a plane closed shape, perimeter of a triangle, perimeter of a square, perimeter of a rectangle, area of a square, area of rectangle, word problems on perimeter of square, word problems on perimeter
Area of a Square | Area of a Square = (Side × Side) Square Units
In area of a square we will learn how to find the area by counting squares. To find the area of a region of a closed plane figure, we draw the figure on a centimeter squared paper and then count the number of squares enclosed by the figure. We know, that square is
Worksheet on Perimeter | Perimeter of Squares and Rectangle | Answers
Practice the questions given in the worksheet on perimeter. The questions are based on finding the perimeter of the triangle, perimeter of the square, perimeter of rectangle and word problems. I. Find the perimeter of the triangles having the following sides.
Worksheet on Area and Perimeter of Rectangles | Word Problems |Answers
Recall the topic and practice the math worksheet on area and perimeter of rectangles. Students can practice the questions on area of rectangles and perimeter of rectangles. 1. Find the area and perimeter of the following rectangles whose dimensions are: (a) length = 17 m
Worksheet on Area and Perimeter of Squares | Questions | Answers
Recall the topic and practice the math worksheet on area and perimeter of squares. Students can practice the questions on area of squares and perimeter of squares. 1. Find the perimeter and area of the following squares whose dimensions are: (a) 16 cm (b) 5.3 m
Worksheet on Volume of a Cube and Cuboid |The Volume of a RectangleBox
We will practice the questions given in the worksheet on volume of a cube and cuboid. We know the volume of an object is the amount of space occupied by the object.1. Fill in the blanks:
Worksheet on Area of a Square and Rectangle | Area of Squares & Rectan
We will practice the questions given in the worksheet on area of a square and rectangle. We know the amount of surface that a plane figure covers is called its area. 1. Find the area of the square length of whose sides are given below: (i) 15 m (ii) 250 m (iii) 25 cm
Volume of a Cuboid | Volume of Cuboid Formula | How to Find the Volume
Cuboid is a solid box whose every surface is a rectangle of same area or different areas. A cuboid will have a length, breadth and height. Hence we can conclude that volume is 3 dimensional. To measure the volumes we need to know the measure 3 sides.
Volume of a Cube | How to Calculate the Volume of a Cube? | Examples
A cube is a solid box whose every surface is a square of same area. Take an empty box with open top in the shape of a cube whose each edge is 2 cm. Now fit cubes of edges 1 cm in it. From the figure it is clear that 8 such cubes will fit in it. So the volume of the box will