Advertisements
Advertisements
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?
Advertisements
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.
APPEARS IN
RELATED QUESTIONS
The diagonal of a square is 12 cm long; find its area and length of one side.
A wire, when bent in the form of a square encloses an area of 484 cm2. Find :
(i) one side of the square ;
(ii) length of the wire ;
(iii) the largest area enclosed; if the same wire is bent to form a circle.
The table given below contains some measures of the square. Find the unknown values.
| Side | Perimeter | Area |
| 6 cm | ? | ? |
1 m = ______ cm.
1 sq m = ______ sq cm.
Avneet buys 9 square paving slabs, each with a side of `1/2` m. He lays them in the form of a square.
- What is the perimeter of his arrangement [Fig (i)]?
- Shari does not like his arrangement. She gets him to lay them out like a cross. What is the perimeter of her arrangement [(Fig (ii)]?
- Which has greater perimeter?
- Avneet wonders if there is a way of getting an even greater perimeter. Can you find a way of doing this? (The paving slabs must meet along complete edges i.e. they cannot be broken.)
If each side of a rhombus is doubled, how much will its area increase?
In the following figure, area of (i) is the same as the area of (ii).
 |
 |
| (i) | (ii) |
Two figures can have the same area but different perimeters.
If the perimeter of a square is 36 cm, what is the length of one side?
