Question

22. In the following figure, find the area of shaded region.

length= 12 cm
breath = 12cm​

Answer 1

Answer:

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

Let us look at the rectangle given below.

Area of Regular Figures

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

 

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 Rectangle

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

Consider the following figures:

(i)

Area of a Rectangle

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Area of each small square = 1 sq cm

Area of rectangle in figure 1 by counting the squares = 6 sq. cm

Area = 6 square cm

Length of rectangle = 3 cm

Breadth of rectangle = 2 cm

Area = 3 × 2 = 6 sq. cm

(ii)  

Area of a Rectangle

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Area of each small square = 1 sq cm

Area of rectangle in figure 2 by counting the squares = 10 sq. cm

Area = 10 square cm

Length of rectangle = 5 cm

Breadth of rectangle = 2 cm

Area = 5 × 2 = 10 sq. cm

Hence, area of rectangle = length × breadth

A = l × b where, A is the area, l and b are length and breadth of a rectangle.

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

Area of Rectangle

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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.

Step-by-step explanation: