Mensuration- Class 6 Maths/ Exercise 10.1/NCERT Solutions.

Chapter 10 of CBSE/NCERT Class 6 Mathematics is about Mensuration. Here in this lesson you can find out text book solutions for Exercise 10.1.

CBSE CLASS 6 MATHEMATICS
MENSURATION – Chapter 10/ Exercise 10.1
Introduction:
PERIMETER: Perimeter is the distance covered along the boundary forming a closed figure when you go round the figure once.
Perimeter of a rectangle = 2 x (length + breadth)
Perimeter of a square = 4 x length of its side
Perimeter of an equilateral triangle = 3 x length of a side
Figures in which all sides and angles are equal are called regular closed figures.
AREA: The amount of surface enclosed by a closed figure is called its area.
Area of a rectangle = length x breadth
Area of a square = side x side
EXERCISE 10.1

1. Find the perimeter of each of the following figures 🙁 For figures look at the text book)
   a) Perimeter = 4 + 2 + 5 + 1 = 12 cm
   b) Perimeter = 23 + 35 + 40 + 35 = 133 cm
   c) Perimeter = 15 + 15 + 15 + 15 = 60 cm
   d) Perimeter = 4 + 4+ 4+ 4+ 4 = 20 cm
   e) Perimeter = 1 + 4 + 0.5 + 2.5 + 2.5 + 0.5 + 4 = 15 cm
   f) Perimeter = 1 + 3 + 2 + 3 + 4 + 1 +3 + 2 + 3 + 4 + 1 + 3 + 2 + 3 + 4 + 1 + 3 + 2 + 3 + 4 = 52 cm
2. The lid of a rectangular box of sides 40 cm by 10 cm is sealed all round with tape. What is the length of the tape required?
   Answer: Length of the tape required = Perimeter of the rectangular box = 2 x (l + b) = 2 x (40 + 10) cm
   = 2 x 50 = 100 cm = 1 m
3. A table-top measures 2 m 25 cm by 1 m 50 cm. What is the perimeter of the table- top?
   Answer;
   Length of the table top = 2 m 25 cm = 2.25 cm
   Breadth of the table top = 1m 50 cm = 1.50 cm
   Perimeter of the table top = 2 x (l + b) = 2 x (2.25 + 1.50) = 2 x 3.75 = 7.50 cm
4. What is the length of the wooden strip required to frame a photograph of length and breadth 32 cm and 21 cm respectively?
   Answer: Given length of the photograph = 32 cm
   Breadth of the photograph = 21 cm
   The length of the wooden strip required = Perimeter of the photograph = 2 x (32 + 21) cm
   = 2 x 53 = 106 cm
5. A rectangular piece of land measures 0.7 km by 0.5 km. Each side is to be fenced with 4 rows of wires. What is the length of the wire needed?
   Answer:
   Given length of the land = 0.7 km
   Breadth of the land = 0.5 km
   Perimeter = 2 x (0.7 + 0.5) = 2 X 1.2 = 2.4 km
   Length of the wire needed = 4 x 2.4 = 9.6 km
6. Find the perimeter of each of the following shapes:
   a) A triangle of sides 3 cm, 4 cm and 5 cm.
   b) An equilateral triangle of side 9 cm
   c) An isosceles triangle with equal sides 8 cm each and third side 6 cm.
   Answer:
   a) Perimeter = 3 + 4+ 5 = 12 cm
   b) Perimeter = 9 + 9 + 9 = 27 cm (All sides are equal)
   c) Perimeter = 8 + 8 + 6 = 22 cm (Two sides are equal)
7. Find the perimeter of a triangle with sides measuring 10 cm, 14 cm and 15 cm.
   Answer: Perimeter = 10 + 14 + 15 = 39 cm
8. Find the perimeter of a regular hexagon with each side measuring 8 m.
   Answer:
   Regular hexagon means all the six sides are equal.
   Perimeter = 6 x 8 = 48 m
9. Find the side of the square whose perimeter is 20 m.
   Answer:
   Given perimeter of the square = 20 m
   One side of the square = 20 / 4 = 5 m
10. The perimeter of a regular pentagon is 100 cm .How long is its each side?
    Answer:
    Given perimeter of a regular pentagon = 100 cm
    (Regular pentagon means all the five sides are equal)
    So length of each side = 100 / 5 = 20 cm
11. A piece of string is 30 cm long. What will be the length of each side if the string is used to form?
    a) a square?
    b) an equilateral triangle
    c) a regular hexagon
    Answer:
    a) Perimeter = 30 cm
    Length of each side of a square = 30 / 4 = 7.5 cm
    b) Length of each side of an equilateral triangle = 30 / 3 = 10 cm
    c) Length of each side of a regular hexagon = 30 / 6 = 5 cm
12. Two sides of a triangle are 12 cm and 14 cm. The perimeter of the triangle is 36 cm. What is its third side?
    Answer:
    Given perimeter of a triangle = 36 cm
    Sum of the two sides of a triangle = 12 + 14 = 26 cm
    Length of its third side = 36 – 26 = 10 cm
13. Find the cost of fencing a square park of side 250 m at the rate of Rs 20 per metre.
    Answer:
    Perimeter of the square park = 4 x 250 = 1000 m
    Cost of fencing = 1000 x 20 =Rs 20000
14. Find the cost of fencing a rectangular park of length 175 m and breadth 125 m at the rate of Rs 12 per metre.
    Answer:
    Perimeter = 2 x (175 + 125) = 2 x 300 = 600m
    Cost of fencing a rectangular park = 600 x 12 = Rs 7200
15. Sweety runs around a square park of side 75 m. Bulbul runs around a rectangular park with length 60 m and breadth 45 m. Who covers less distance?
    Answer:
    Perimeter of a square park = 4 x side = 4 x 75 = 300 m
    Perimeter of a rectangular park = 2 x (60 + 45) = 2 x 105 = 210 m
    Therefore, Bulbul covers less distance.
16. What is the perimeter of each of the following figures? What do you infer from the answers?
    a) Perimeter = 25 x 4 = 100 cm
    b) Perimeter = 2 x (l + b) = 2 x (40 + 10) = 2 x 50 = 100 cm
    c) Perimeter = 30 + 20 + 30 + 20 = 100 cm
    d) Perimeter = 30 + 30 + 40 = 100 cm
    All the figures have same perimeter.
17. Anveet buys 9 square paving slabs, each with a side of ½ m. He lays them in the form of a square.
    a) What is the perimeter of his arrangement?
    b) Shari does not like his arrangement. She gets him to lay them out like a cross. What is the perimeter of her arrangement?
    c) Which has greater perimeter?
    d) Anveet wonders if there is a way of getting an even greater perimeter. Can you find a way of doing this?
    Answer:
    a) Side of square = 3 x ½ =3/2 m
    Perimeter of square = 4 X 3/2 = 12/2 = 6 m
    b) Perimeter of cross = 0.5 + 1 + 1 + 0.5 + 1 + 1 + 0.5 + 1 + 1 +0.5 + 1 + 1 = 10m
    c) The arrangement in the form of a cross has a greater perimeter.
    d) If all the squares arranged in a row, then the perimeter will be 10 cm.