Question

The area of a square is greater than two times the area of a rectangle by 16 cm sq. if the length of the rectangle is 4cm less than the side of the square, which is 24cm. what is the perimeter of the rectangle ?

Answer 1

Area of a rectangle is discussed here. We know, that a rectangle has length and breadth.

Let us look at the rectangle given below.

Each rectangle is made of squares. The side of each square is 1 cm long. The area of each square is 1 square centimeter.

Let us find the area of a rectangle having length 5 cm and breadth 4 cm.

From the above figure, it is clear that we can divide this rectangle into 20 squares of sides 1 cm each. SO, the area = 20 cm2

Thus the area of the rectangle = 5 cm × 4 cm

= 20 cm2

So when we multiply its length and breadth we get the area of the rectangle.

The rectangle ABCD has 8 such squares. Therefore, its area is 8 sq cm. Similarly we can find the areas of the other rectangles by counting the number of squares. We also note the length and breadth of each rectangle and write in the table below:

Rectangle

ABCD

LMNO

PQRS

Area

8 sq. cm

12 sq. cm

6 sq. cm

Length

4 cm

4 cm

2 cm

Breadth

2 cm

3 cm

3 cm

Length × Breadth

4 cm × 2 cm = 8 cm2

4 cm × 3 cm = 12 cm2

2 cm × 3 cm = 6 cm2

In each case we observe the length × breadth = Area of the rectangle.

Therefore, area of rectangle = length × breadth = l × b sq. units

From the above multiplication, we get the following facts:

Length of the rectangle = Area of the RectangleBreadth of the RectangleArea of theRectangleBreadth of the Rectangle

Breadth of the rectangle = Area of the RectangleLength of the RectangleArea of theRectangleLength of the Rectangle


Solved examples to find the area of a rectangle when length and breadth are given:

1. Find the area of a rectangle of length 12 cm and breadth 3 cm.

Length (l) of the rectangle = 12 cm.

Breadth (b) of the rectangle = 3 cm.

Area of the rectangle = length × breadth 

                               = 12 × 3 sq cm.

                               = 36 sq cm.


2. Find the area of a rectangle of length 15 cm and breadth 6 cm.

Length of the rectangle = 15 cm.

Breadth of the rectangle = 6 cm.

Area of the rectangle = l × b

                               = 15 × 6 sq cm.

                               = 90 sq cm.


3. Find the area of a rectangle of length 17 cm and breadth 9 cm.

Length of the rectangle = 17 cm.

Breadth of the rectangle = 9 cm.

Area of the rectangle = l × b

                               = 17 × 9 sq cm.

                               = 153 sq cm.


4. Find the area of a rectangle of length 24 mm and breadth 8 mm.

Length of the rectangle = 24 mm.

Breadth of the rectangle = 8 mm.

Area of the rectangle = l × b

                               = 24 × 8 sq mm.

                               = 192 sq mm.


5. Find the area of a rectangle of length 37 mm and breadth 19 mm.

Length of the rectangle = 37 mm.

Breadth of the rectangle = 19 mm.

Area of the rectangle = l × b

                               = 37 × 19 sq mm.

                               = 703 sq mm.