AREA OF RECTANGLE

On this page "area of rectangle", we are going to see how to find the area of any rectangle. Here we give clear explanation about rectangle.

Definition of rectangle

A plane figure with four straight sides and four right angles.In which the opposite sides are having the same length.

Formula:

Area of rectangle  =  L x B

Here "L" represents length of the rectangle and "B" represents the breadth of the rectangle.

Problem 1:

Find the area of the rectangle whose length is 15 cm and breadth is 20 cm.

Solution:

Area of a rectangle  =  L x B

Here length (l) = 15 cm and breadth = 20 cm

 =  15 x 20  

=  300 cm²

Problem 2:

Find the area of the rectangle having the diagonal is measuring 13 cm and length measuring 12 cm.

Solution:

The diagonal divides the rectangle into two right triangle. In the right triangle ABC the right angled at B.

The side which is opposite to 90°degree is called hypotenuse side. By using Pythagorean theorem

AC² = AB² + BC²

13² = 12² + BC²

169 = 144 + BC²

169 - 144 = BC²

25 = BC²

BC = √25

BC = √5 x 5

BC = 5

So, breadth of the rectangle = 5 cm

Area of the rectangle = Length x Breadth

                             = 12 x 5

                             = 60 cm²

Problem 3:

The length and breadth of the rectangle are in the ratio 5:2 .If the area of the rectangle is measuring 147 cm². Then find the length and breadth of the rectangle.

Solution:

5x and 2x be the length and breadth of the rectangle respectively.

Area of the rectangle = 147 cm²

Length x breadth  =  147

5x x 2x  =  147

7x²  =  147

x²  =  147/7

x²  =  21

x  =  √21   

Length  =  5x  =  5√21 cm

Breadth  =  2x  =  2√21 cm

Problem 4:

Find the cost of carpeting a room 13 m long and 9 m broad with a carpet 75 cm wide at the rate of $12.40 per square meter.

Solution:

From the given information we come to know that

Area of carpet  =  Area of room  ---- (1) 

area of rectangle  =  length  x breadth

0.75 x breadth of carpet  =  13 x 9

breadth of carpet  =  (13 x 9) /0.75

=  117/0.75

=  156 m

Cost of carpeting = 156 x 12.40 = $ 1934.40

Problem 5:

If the diagonal of a rectangle is 17 cm long its perimeter is 46 cm, find the area of rectangle.

Solution:

Let "x" and "y" be the length and breadth of the rectangle respectively.

perimeter of rectangle = 46

2 (x + y) = 46

     y = 23 - x -----(1)

 x² + y² = 17²  

 x² + y² = 289  -----(2)

Substitute (1) in the second equation

 x² + (23- x)² = 289

 x² + (23)² + x² - 2 (23)(x) = 289

2x² - 46x + 529 - 289 = 0

2x² - 46 x + 240 = 0

 divide the whole equation by 2

 x² - 23 x + 120 = 0

(x - 15) (x - 8) = 0

 x = 15   x = 8

 y = 23 - 15           y = 23 - 8

 y = 8  y = 15

So, length of rectangle = 15 m and

breadth of rectangle= 8 m 

More shapes

Square Area of square Perimeter of square Parallelogram Area of parallelogram Perimeter of parallelogram

Rectangle Area of rectangle Perimeter of rectangle  Rhombus Area of rhombus Perimeter of rhombus

Traingle Area of equilateral triangle Area of scalene triangle  Area of right triangle Quadrilateral Area of quadrilateral Sector Examples problems on area of sector Examples problems on length of arc Worksheet for length of arc Perimeter of sector worksheets Area of sector worksheet Hollow cylinder Example problems of curved surface area  More example problems of curved surface area Sphere Example problems of sphere Area around circle Area around circle example problems Area of combined figures Example problems of area of combined figures

Trapezium Area of trapezium Circle Area of circle Circumference of circle  Semicircle Example problems of semicircle  Quadrant Example problems on quadrant Cyclinder Examples problems of cylinder Cone Example problems of Cone  Hemisphere Example problems of hemisphere Path ways Area of path ways