Perimeter and Area

MENSURATION

Points to remember:

Perimeter and Area 

Perimeter

 Perimeter of any closed figure is the distance covered along its boundary.

Perimeter of any closed figure = The sum of the lengths of its all sides.

(i) Perimeter of a Triangle = The sum of the lengths of its all sides.

AB = a 

BC = b 

AC = c 

Perimeter of a ∆ABC = AB+ BC + CA

                                     = a + b + c

(ii) Perimeter of rectangle ABCD = The sum of the lengths of its all sides.

AB = l 

BC = b

CD = l

DA = b

Perimeter of Square ABCD = AB+BC+CD+DA

Square 

Perimeter of Square = l + b + l + b

Perimeter of Square = 2l + 2b

Perimeter of Square = 2(l + b)

(iii) Perimeter of Square ABCD = The sum of the lengths of its all sides.

AB = a 

BC = a 

CD = a 

DA = a

Perimeter of Square ABCD = AB+BC+CD+DA

Square 

Perimeter of Square = a + a + a + a

Perimeter of Square = 4 × a

Perimeter of a pentagon ABCDE = AB+BC+CD+DE+EA

Perimeter of ABCDE = AB+BC+ CD + DE + EA

(iii) Unit of Perimeter can be Unit as, mm (millimetre), cm (centimetre), m (metre), km (kilometre) etc.

Regular Polygons

(i) Figures, in which all sides and all angles are equal, are called regular polygons.

Finding perimeter of regular closed figure when length is given 

Perimeter of regular closed figure = n x length of side 

(where 'n' is number of sides of the regular closed figure)

Finding Length of regular closed figure when perimeter is given 

n of sides × length of side  = Perimeter of n-gon

where 'n' is number of sides of the regular closed figure

(iii) Perimeter of Equilateral triangle = 3 x length of side

(iv) Perimeter of square = 4 × length of side

(v) Perimeter of regular pentagon = 5 × length of side

(vi) Perimeter of regular hexagon = 6 x length of side

(vi) Perimeter of regular hexagon = 6 x length of side

Perimeter of Rectangle = 2× (Length + Breadth)

Area

(1) Area of any closed figure is the surface enclosed by its boundary.

(ii) Area of PQRS = Shaded portion

(iii) Unit of area can be Unit² or square unit as mm² (square millimetre), cm² (square centimetre), m² (square metre), km² (square Kilometre) etc.

Area of Rectangle = Length x Breadth

Or

Length × Breadth = Area of Rectangle

(i) Length = Area of Rectangle / Breadth

(i) Breadth = Area of Rectangle / Length

Area of Square = Side x Side

                                         Area of floor/wall 

The Number Of Tiles = -------------------------------

                                             Area of 1 tile 

Questions:

1. Find the perimeter of regular octagon with length of each side of 2 cm.

2. Neena swims along with boundary of a pool with the measurements of length 12 feet and width 8 feet. Find perimeter of pool.

3. Find the area of figure if, each box is a square of side 1 cm.

4. Kajal has a polygon with sides 5 cm, 3 cm and 7 cm. What is the name of this polygon and what is its perimeter?

5. What is the perimeter of a rectangle whose length is 7.5 m and breadth is 2.7 m?

6. Find perimeter of the figure.

7. Find the width of the rectangle whose area is 209 sq. m and length is 19 m.

8. Find the length of that rectangle whose area is 4200 sq. m and width is 35 m.

9. A girl walks around a regular pentagon with side 350 m. She took 3 complete rounds. Find the distance covered by her.

10. What is the perimeter of a rectangle whose length is 1225 cm and breadth is 1 m?

11. What is the cost of fencing of a garden with dimensions 400 m x500 m at the rate of 20 per metre?

12. Shree bought 8 Km long wire to fence his field. If field is 1.5 km long and 2 km wide, how much wire will be left after fencing?

13. What is the cost of fencing the park with sides given below, if the cost of fencing is 20 per metre?

14. Sakshi has 1 m lace. She uses it to put it around a square hanky which had one side equal to 17.5 cm. How much lace will be left?

15. A box has 6 square faces which are to be painted. Each face has side of 5 m. What will be the cost of painting at the rate of 3 per sq m?

16. What will be the length of rectangular wooden strip required to frame a picture whose length is 4 m 25 cm and width 65 cm?

17. The perimeter of a triangle is 62 cm. What is the measure of third side of the triangle if the measure of two sides is 27 cm and 14 cm?

18. Find the value of x in the given figure, if the perimeter of the figure is 200 cm.

19. Find y, if perimeter of the figure is 38 cm.

20. An isosceles triangle has a perimeter of 54 cm. If the measure of unequal side is 21 cm, then what will be the measure of each of the two equal sides?

21. Each table in a classroom is 80 cm long and 50 cm wide. There are 15 tables in a classroom. Find the total area of tables.

22. What is the perimeter of a square if its aren is 36 sq. cm?

23. The length and breadth of a rectangle are 24 cm and 8 cm respectively. If its length is doubled and breadth is halved, then what is its new area?

24. The area of a rectangle is 12 sq cm. If its length is doubled and breadth is halved, then what is its new area?

25. Measurement of a curtain for Manesh's room is 8mx2m.What will be the area of window covered with this curtain?

26. The length of a rectangle is thrice its breadth. If its perimeter is 80 m, then what is its area?

27. The length of a rectangle is twice its breadth. If its area is 128 s wh is its perimeter?

28. The screen of a TV measures 32 inches in length and its area is 640 sq inches. What is the width of the screen?

29. What is the area of the given figure?

30. Mr. X wishes to carpet his room. Room is 15 ft long and 12 ft wide. How many square feet of carpet does he need to buy?

31. If length of a rectangle is 6.5 cm and its area is 2600 sq cm then, find its width in meter.

32. What is the cost of tiling a rectangular floor with length 40 m and breadth 30 m at the rate of 5 per square metre?

33. A pentagon has 3 sides of same length and 2 side with different length. The 3 equal sides are 8 cm long. The other 2 side are 11 cm and 6 cm long respectively. What is its perimeter?

34. What is the area of the shaded portion in the given figure?

35. If the perimeter of two squares are 36 cm and 44 cm respectively. What will be the side of the square whose perimeter is equal to the sum of the perimeters of these two squares?

36. If the perimeter of three squares are 48 cm, 28 cm and 44 cm respectively. What will be the side of the square whose perimeter is equal to the sum of the perimeters of these three squares?

37. If the perimeter of two squares are 24 cm and 52 cm. What will be the area of the square whose perimeter is equal to the sum of the perimeters of these two squares?

38. If the area of two squares is 36 sq. cm and 64 sq. cm respectively. What will be the side of the square whose perimeter is equal to the sum of the perimeters of these two squares?

39. If the area of two squares is 9 sq. cm and 16 sq. cm respectively. What will be the perimeter of the square whose area is equal to the sum of the areas of these two squares?

40. In a square park of side 15 m, four squared flower beds each side 5 m are to be made as shown in figure. What is the area of remaining part of the park without flower beds?

41. What is the perimeter of 10-sided regular polygon whose length of each side is 3.5 m?

42. What is the distance travelled in taking 3 rounds of a regular pentagon of side 5 m?

43. What will be the area of shaded portion in the figure?

44. The perimeter of an equilateral triangle is 87 cm. What is the length of its each side?

45. What is the area of the figure given below?

46. Mohan wants to cover the floor of a room 3 m wide and 4 m long by square tiles. If each tile is of side 0.5 m, then calculate the number of tiles he want to buy.

47. A square of 100 m side can be divided into how many rectangles of size 2 mx 1 m?

48. A man wants to paint walls of his room. Measurement of wall of the room is 3 mx 2 m. what is the total area to be painted? A can of paint covers 10 sq m. How many cans are needed if each wall needs 2 coats of paint?

49. Leela has a rectangular garden that measures 10 km ×12 km. she wants to plant apples in her garden. If one seed packet is enough to fill 40 sq km then, how many packets are needed for her garden?

50. A farmer planted vegetables in a rectangular garden that was 20 feet long and 45 feet wide. He used of the area for brinjals and of it for planting 3 potatoes. How many sq feet are left for other vegetables?