Perimeter of Square and Rectangle

Q. What is the formula of area and perimeter of square, rectangle and triangle?

Q.

The perimeter of a rectangle is $130cm$. If the breadth of the rectangle is $30cm$, find its length. Also, find the area of the rectangle.

Q.

If the side of a square is doubled, its perimeter becomes ………

1. double

2. $3$times

3. $4$times

4. $8$times

Q.

A piece of wire $40\mathrm{cm}$ long is to be cut into two pieces.

One-piece will be bent to form a circle; the other will be bent to form a square.

$\left(a\right)$ Find the lengths of the two pieces that cause the sum of the area of the circle and the area of the square to be a minimum.

$\left(b\right)$ How could you make the total area of the circle and the square a maximum.

Q.

The perimeter of a rectangle becomes __________ times its original perimeter if its length and breadth are doubled.

Q. Perimeter of a square of side 4cm is ______cm .

1. 16

Q. The length of a rectangle is twice its breadth. What is the length and breadth of the rectangle if its perimeter is 6 cm?

1. 2cm, 1cm
2. 3cm, 2cm
3. 1cm, 2cm
4. 2cm, 2cm

Q. Perimeter of a rectangle of length l and breadth b is __________ .

1. 2(2l+b)
2. 2(l+b)
3. l+b
4. lb

Q. The area of a rectangular garden of length 40 m, is 1000 sqm. Find the breadth of the garden and its perimeter. The garden is to be enclosed by 3 rounds of fencing, leaving an entrance of 4 m. Find the cost of fencing the garden at a rate of 250 rupees per metre.

Q.

How many envelopes can be made out of a sheet of paper 100 cm by 75 cm, supposing 1 envelope requires 20 cm by 5 cm piece of paper?

1. 75

2. 50

3. 100

4. 25

Q. The perimeter of a rectangle is 230 cm. If the length of the rectangle is four times the breadth, what is the breadth of the rectangle?

1. 18 cm
2. 20 cm
3. 21 cm
4. 23 cm

Q.

If the length of the diagonal of a square is $12\sqrt{2}cm$, what is its perimeter?

1. 54 cm

2. 38 cm

3. 44 cm

4. 48 cm

Q.

How much wire will be required to fence a square field of area 441 square meters?

1. 441 m

2. 21 m

3. 84 m

4. 48 m

Q.

If the area of a rectangle is equal to the area of a square and the length of the rectangle is equal to the perimeter of the square, then the breadth of the rectangle is

1. $\raisebox{1ex}{$\mathrm{side}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

2. $\raisebox{1ex}{${\mathrm{side}}^2$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$

3. $\raisebox{1ex}{$\mathrm{side}$}\!\left/ \!\raisebox{-1ex}{$4$}\right.$

4. $\raisebox{1ex}{$\mathrm{side}$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$

Q.

The area of a square with side length 7 m is ___$m^2$.

Q. Find the area of the rectangle whose length is 100 cm and perimeter is 300 centimetres

Q.

If the perimeter of the rectangular field is $200m$ and its breadth is $40m,$ then its area is $\_\_\_\_$

Q.

Side of a square garden is $30m$. If the scale used to draw its picture is $1cm:5m$, the perimeter of the square in the picture is

1. $24cm$

2. $20cm$

3. $28cm$

4. $30cm$

Q.

A wire is in the form of a circle of radius $35\mathrm{cm}$. It is now bent in the form of a square, Find the area of the square.

Q. The length and breadth of a rectangular courtyard is 45 m and 35 m respectively. Find the distance covered by a boy to take 5 rounds of the courtyard.

1. 200 m
2. 600 m
3. 800 m
4. 400 m

Q.

In a four sided field, the length of the longer diagonal is 128 m. The lengths of the perpendiculars from the opposite vertices on this diagonal are 22.7 m and 17.3 m. Find the area of the field. [4 MARKS]

Q.

The area of a square of side length 'x' is $x^2$.

1. True

2. False

Q. If area of a square is equal to area of a rectangle whose length and breadth are 9 cm and 4 cm respectively, then find the perimeter of the square.

Q.

A square shaped picture is to be framed.

Its side is $29cm$. What length of the frame will be required?

Q.

The area of a rectangle is $16sqcm,$then what are the possible dimensions of the rectangle?

Q.

A square lawn has each side 12.25m long. Find the distance all round it.

Q.

A piece of square land has a perimeter equal to 20 m. A cow is standing in the middle of the square land as shown in the figure. What is the minimum distance the cow has to travel in order to go out of the field and drink water?

1. 5 m

2. 2.5 m

3. 4 m

4. 20 m

Q.

If the area of a rectangular plot is $144m^2$ and its length is $16m$. Find the breadth of the plot and the cost of fencing it at the rate of $₹6permetre$.

Q.

A circle is divided into 8 equal parts. Given that the area of the shaded portion is $\frac{10}{4}$ $m^2$. Find the area of the unshaded part of the circle.

[4 MARKS]

Q.

A square and a rectangle are of equal area. If the perimeter of rectangle is $p$ and that of a square is $q$, then

1. $p=q$

2. $p<q$

3. $p>q$

4. $p\le q$