Question

In the following figure, each square is of unit length

1. What is the perimeter of the rectangle ABCD?
2. What is the area of the rectangle ABCD?
3. Divide this rectangle into ten parts of equal area by shading squares. (Two parts of equal area are shown here)
4. Find the perimeter of each part which you have divided. Are they all equal?

 

Answer 1

Given, each side of square is of unit length.

Figure contains length of 10 squares and width of 6 squares.

Now, length of rectangle, AD = BC

= Sum of length of a side of 10 squares

= 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1

= 10 × 1

= 10 units and breadth of rectangle, AB = DC

= Width of 6 squares

= 6 × 1

= 6 units

a. The perimeter of the rectangle ABCD

= AB + BC + CD + DA

= 6 + 10 + 6 + 10

= 32 units

b. The area of the rectangle ABCD

= Length × Breadth

= AD × AB

= `600/10`

= 60 sq.units

c. The total area of rectangle = 60 sq.units.

Now, we have to divide the rectangle into 10 equal parts i.e., 6 × 1 = 6 square units, i.e., we have to take a group of 6 – 6 square blocks, which is shown in the figure.

d. Now, we find the perimeter of part I.

We know that perimeter of a figure is the total length of its boundary.

Perimeter of part 1 = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 12 units.

Similarly, we can find the perimeters of remaining 9 parts, all the parts have same perimeter, i.e., 12 units.

Yes, all the parts have same perimeter.