Worksheet on Area and Perimeter of Rectangle Problems will help the students to explore their knowledge of Rectangle word Problems. Solve all the Problems to learn the formula of Area of Rectangle and Perimeter of a Rectangle. To know the definition, properties, derivation, Problems with Solutions, Formulas of Rectangle you can visit our website. We have given the complete Rectangle concept along with examples. Check out the Area and Perimeter of Rectangle Problems Worksheet and know the various strategies to solve problems in an easy and understandable way.

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## Perimeter and Area of a Rectangle – Definitions

A Rectangle is a quadrilateral with two equal sides and two parallel lines and four right angles. Four right angles vertices are equal to 90 degrees, it is also called an equiangular quadrilateral.

The perimeter of the rectangle is defined as the sum of all the sides of the rectangle. Rectangle has two lengths and breadths, it is denoted by P, it is measured in units. For finding the perimeter of the rectangle we have to add the length and breadth.

Perimeter of the Rectangle, P = 2(l + b)

The area of the rectangle is defined as to calculate the length and breadth of the two- dimensional closed figure. For finding the area of the rectangle we have to multiply the length and breadth, it is denoted by A, measured in square units.

Area of the rectangle , A = l x b

### Problems on Area and Perimeter of the Rectangle

1. Find the Area and Perimeter of the following rectangles whose dimensions are :

(i) length = 15 cm breadth = 12 cm

(ii) length = 7.9 m breadth = 6.2 m

(iii) length = 4 m breadth = 36 cm

(iv) length = 2 m breadth = 6 dm

## Solution:

(i) Given, length = 15 cm, breadth = 12 cm

we know that, Perimeter of rectangle = 2 (length + breadth)

substitute the given values in above formula, we get

Perimeter of rectangle = 2 (15 + 12) cm

= 2 × 27 cm

= 54 cm

We know that, area of rectangle = length × breadth

Therefore, substituting the values in above formula, we get

Area of rectangle = 15 cm x 12 cm

= (15 × 12) cm²

= 195 cm²

Therefore, Area of rectangle is 195 cm²

(ii) Given, length = 7 m, breadth = 6.2 m

we know that, Perimeter of rectangle = 2 (length + breadth)

substitute the values in the formula , we get

Perimeter of rectangle = 2 (7.9 + 6.2) m

= 2 × 14. 1 m

= 28. 2 m

We know that, area of rectangle = length × breadth

Therefore, substituting the value we get,

Area of rectangle = 7.9 m x 6.2 m

= (7.9 × 6.2) m²

= 48. 98m²

Therefore, Area of rectangle = 48. 98 m²

(iii) Given, length = 4 m

breadth = 36 cm = 36/ 100 = 0. 36 m ( cm is converted to m)

we know that, Perimeter of rectangle = 2 (length + breadth)

substitute the values in the formula, we get

Perimeter of a rectangle = 2 (4 + 36) m

= 2 × 40 m

The perimeter of a rectangle is 80 m

We know that, area of rectangle = length × breadth

substituting the value we get,

Area of rectangle = 4 m× 36 m

= (4 x 36) m²

= 144 m²

Therefore, Area of a rectangle is 144 m²

(iv) Given, length = 2 m

breadth = 60 dm

1m = 10 dm

so we get, 60 dm = 6 m ( dm is converted to m)

we know that, Perimeter of rectangle = 2 (length + breadth)

substitute the values in the formula, we get

Perimeter of rectangle = 2 (2 + 6) m

= 2 × 8 m

= 16 m

We know that, area of rectangle = length × breadth

substituting the value we get,

Area of rectangle = 2 m× 6 m

= (2x 6) m² = 12 m²

Therefore, the Area of a rectangle is 12m².

2. The perimeter of the rectangle is 140 cm. If the length of the rectangle is 30 cm, find its breadth and area of the rectangle?

## Solution:

Given, Perimeter of the rectangle is, 140 cm

The length of the rectangle is, 30 cm

we know that, Perimeter of the rectangle = 2(l + b)

substitute the value in the above formula, we get

140 = 2( 30 + b)

70 = 30

40 = b

Therefore, breadth = 40 cm

Now, Area of Rectangle = length x breadth

= 30 x 40 = 120 cm²

Therefore, the Area of a rectangle is 120 cm²

3. The area of a rectangle is 78 cm². If the breadth of the rectangle is 6 cm, find its length and perimeter?

## Solution:

Given, Area of a rectangle is 78 cm²

The breadth of the rectangle is 6 cm

we know that, Area of rectangle = length x breadth

substitute the given value, we get

78 cm = length x 6 cm

78/ 6 = length

Length of the rectangle =12 cm

Now, perimeter of rectangle = 2 (l + b)

substitute the value, we get

Perimeter of rectangle = 2(12 + 6)

= 2 x 18

= 36 cm

Therefore, the perimeter of the rectangle = 36 cm

4. How many boxes whose length and breadth are 9 cm and 5 cm respectively are needed to cover a rectangular region whose length and breadth are 420 cm and 90 cm?

## Solution:

Given, Length of the box is 9 cm

The breadth of the box is 5 cm

Region length is 420 cm

Region breadth is 90 cm

we know the formula,

The area of a rectangle is l x b

Therefore, Area of region = l x b

substitute the value, we get

Area of region = 420 cm x 90 cm

= 37800 cm²

Again use the area of a rectangle formula,

Area of one box is = 9 cm x 5 cm

= 45 cm²

Number of boxes = Area of region /Area of one box = 37800/45 = 840

Thus, 840 boxes are required.

5. If it costs $500 to fence a rectangular park of length 40 m at the rate of $25 per m², find the breadth of the park and its perimeter. Also, find the area of the field?

## Solution:

Given, Cost of Rectangular park fencing is $500

Length of the rectangular park = 20 m

Rate of fencing 1 m² = $25

Area of a rectangle = l x b

Now we find area , therefore Area = 500/ 25 = 20

substitute the value in formula, we get

20 = 20 x breadth

breadth = area / length

b = 20 / 20 = 1 m

Now finding the Perimeter,

Perimeter of a rectangle = 2 (l + b)

substituting the values ,

Perimeter of a rectangle= 2 (20 + 1)

= 2 (21)

Therefore, the Perimeter of a rectangle = 41 m

6. A rectangular tile has a length equals to 20 cm and a perimeter equals 70 cm. Find its width?

## Solution:

Given, Perimeter of the tile = 80 cm

Length of the tile = 20 cm

Let W be the width of the tile

we know that,

Perimeter of a rectangle = 2(length + width)

Substituting the values, we get,

The perimeter of a tile = 80 cm

Therefore, 80 = 2 (20 + Width)

80/ 2 = 20 + Width

40 = 20 + Width

40 – 20 = Width

Therefore, Width = W = 20.

7. Find the area of a rectangle, Perimeter of a rectangle, and diagonal of a rectangle whose length and breadth 12 cm and 16 cm respectively.

## Solution:

Given, length of the rectangle = 12 cm

Breadth of the rectangle = 16 cm

we know the formulae,

Area of a rectangle = l x b

substitute the values in the above formula, we get

Area of a rectangle = 12 x 16 = 192 cm²

we know, Perimeter of a rectangle = 2 (l + b)

substitute the values, we get

Perimeter of a rectangle = 2 (12 + 16)

= 2 (192) = 384 m

Now, we finding the diagonal of a rectangle

The diagonal of a rectangle is d² = l² + b²

substitute the values, we get

d² = (12)² + (16)²

d² = (12 + 16)²

d = √(12 + 16)²

square and root both will be cancelled,

d = 12 + 16 = 28

Therefore, the Diagonal of a rectangle = 28 cm.

8. Find the cost of tiling a rectangular plot of land 200 m long and 120 m wide at the rate of $6 per hundred square m?

## Solution:

Given,

Cost of tiling rectangular plot of land 200 m long and 120 m wide

The cost of tiling per 100 sq.m is $6

we know the area of a rectangle formula,

Area of a rectangle = length x breadth

substituting the values in the above formula, we get

Area of a rectangle = 200 m x 120 m

= 24000 m²

Therefore, the Area of a rectangle is 24000 m²

Now, we finding the total cost of tiling

Total cost of tiling = (6 x 24000) / 100

= 144000/100

= $1440

Therefore, the Total cost of tiling is $1440

9. The length of a rectangular board is thrice its width. If the width of the board is 140 cm, find the cost of framing it at the rate of $5 for 30 cm.

## Solution:

Given, the width of the board = 140 cm

length of the board is thrice

so ,length = 3 x width

length = 3 x 140 = 420 cm

30 cm rate is $5

Circumference of rectangle = 2 ( l+ b)

substitute the values in the above formula, we get

Circumference of rectangle = 2 ( 420 + 140)

= 2 x 560 = 1120 cm

Therefore, the circumference of rectangle = 1120 cm

Now, 30 cm cost is equal to rs. 5

So, 1 cm = 5/ 30

But, we want the cost of framing

So, 1120 = (5 x 1120)/ 20 = rs. 280

Therefore, the cost of framing is Rs. 280

10. The Perimeter of a rectangular pool is 46 meters. If the length of the pool is 16 meters, then find its width. Here the perimeter and length of the rectangular pool are given. we have to find the width of the pool.

## Solution:

Given,

The perimeter of a rectangular pool is 46 meters

The length of the pool is 16 meters

Now we find the width of the pool.

we know the formula,

Perimeter of a rectangle = 2(l + b)

substituting the values, we get

46 = 2( 16) +2( w)

46= 32 + 2w

46 – 32 = 2W

14 = 2W

W= 14/2 = 7 meters

Therefore, the width of the Pool is 7 meters.

11. The sides of a rectangle are in the ratio of 4: 5 and its perimeter is 90 cm. Find the dimensions of the rectangle and hence its area.

## Solution:

Given, Perimeter of a rectangle is 90 cm

Length of the sides = 4 : 5

Let the common ratio be X

So the sides will be 4X and 5X

we know that,

The Sum of all sides of the rectangle is equal to the perimeter.

so, Perimeter of a rectangle = 2 ( length + breadth)

substituting the values, we get

90 = 2(l) + 2(b)

90 = 2(4X) + 2 (5X)

90 = 8X + 10 X

18 X = 90

Therefore, X = 90/18 = 5

Hence , length = 4X and breadth = 5X

substitute the ‘X’ value, we get

length = 4(5) = 20 , Breadth = 5(5) = 25

Now we find the area of a rectangle,

Area of a rectangle = length x breadth

substitute the values in the formula, we get

Area of a rectangle = 20 cm x 25 cm

= 500 cm²

Therefore, the Area of a rectangle is 500 cm².