Problems on Square, Rectangle and Circle

Problems to Solve on Mensuration

1.      Find the perimeter of the following rectangles.

a.       Rectangle ABCD in which AB = 20 cm, BC = 15 cm.

b.      Rectangle PQRS in which PQ = 18 cm, QR = 12 cm.

2.      Kayla wants to build a fence in her backyard. The length of her backyard is 30 feet and the width is 45 feet. How many feet of fence will she need to buy?

3.      The area of a soccer field is 56 square yards. The length of one side of the field is 8 yards. What is the width of the field?

4.      Farmer John walks his pet pig around his barn every day. The barn is 25 meters by 12 meters. If he makes the pig walk around the barn three times, how many meters did farmer John and his pig walk?

5.      If the area of a basketball court in 117 square feet and the width is 9 feet, what is the length?

6.       Jenny's room is 13 feet long and 12 feet wide. Ruth's room is 14 feet long and 11 feet wide. Whose room has the greater perimeter?

7.      Stephen has a rectangular bedroom with a perimeter of 34 feet. The length of the bedroom is 9 feet. What is the width of Stephen's bedroom?

8.      A living room wall is 20 feet long, and 12 feet high. How much paint do you need to cover one wall?

9.       If a rectangle is 9 cm by 2 cm, what is its perimeter?  What is its area?  

10.  Penny's garden has a fountain in the middle that has a base of 5 in. and the height is 9 in. The garden around it has a base of 16 in. and the height is 5 in. What is the area of the garden excluding the fountain?

11.  The length and the breadth of a rectangular piece of land are 500 m and 300 m respectively. Find its area.

12.  Find the breadth of a rectangular plot of land, if its area is 440 m² and the length is 22 m. Also find its perimeter.

13.  The perimeter of a rectangular sheet is 100 cm. If the length is 35 cm, find its breadth. Also find the area.

14.  The area of a square park is the same as of a rectangular park.  If the side of the square park is 60 m and the length of the rectangular park is 90 m, find the breadth of the rectangular park.

15.  A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm.  If the same wire is rebent in the shape of a square, what will be the measure of each side. Also find which shape encloses more area?

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

17.  A door of length 2m and breadth  1m is fitted in a wall. The length of the wall is 4.5 m and the breadth is 3.6 m. Find the cost of white washing the wall, if the rate of white washing the wall is Rs. 20 per m².

18.  Kannan divides a circular disc of radius 14 cm into four equal parts.  What is the perimeter of a quadrant shaped disc?

19.  A Rose garden is in the form of circle of radius 63 m.  The gardener wants to fence it at the rate of ₹150 per metre.  Find the cost of fencing?

20.  A wire of length 1320 cm is made into circular frames of radius 7 cm each. How many frames can be made?

Points to Remember:

1.       Perimeter is the distance around a closed figure whereas area is the part of plane occupied by the closed figure.

2.      Formula to find perimeter and area of a square and rectangle are as follows:

a.       Perimeter of a square = 4 × side

b.      Perimeter of a rectangle = 2 × (length + breadth)

c.       Area of a square = side × side

d.      Area of a rectangle = length × breadth

3.      The distance around a circular region is known as its circumference.

a.       Circumference of a circle = πd, where d is the diameter of a circle and π = 22/7 or 3.14 (approximately).

b.      Area of a circle = πr², where r is the radius of the circle.

Answers:

1.               a. 70 cm
b. 60 cm