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Question
In the following figure, each square is of unit length
- What is the perimeter of the rectangle ABCD?
- What is the area of the rectangle ABCD?
- Divide this rectangle into ten parts of equal area by shading squares. (Two parts of equal area are shown here)
- Find the perimeter of each part which you have divided. Are they all equal?
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Solution
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.
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