# NCERT Solutions for Class 6 Maths Chapter 10 Mensuration Ex 10.1

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Textbook | NCERT |

Board | CBSE |

Category | NCERT Solutions |

Class | Class 6 |

Subject | Maths |

Chapter | Chapter 10 |

Chapter Name | Mensuration Ex 10.1 |

Number of Questions Solved | 6 |

## NCERT Solutions for Class 6 Maths Chapter 10 Mensuration Ex 10.1

**NCERT TEXTBOOK EXERCISES**

**Question 1. Find the perimeter of each of the following figures:**

**Solution :**

**(a) **Perimeter

= 5 cm + I cm + 2 cm + 4 cm

= 12 cm**(b)** Perimeter

= 40 cm + 35 cm + 23 cm + 35 cm

= 133 cm**(c)** Perimeter

= 15 cm + 15 cm + 15 cm+ 15 cm

= 60 cm**(d)** Perimeter

= 4 cm + 4 cm + 4 cm + 4 cm + 4 cm

= 20 cm**(e)** Perimeter

= 1 cm + 4 cm + 0.5 cm + 2.5 cm + 2.5 cm + 0.5 cm + 4 cm

= 15 cm**(f)** Perimeter = 1 cm + 3 cm + 2 cm + 3 cm + 4 cm + 1 cm + 3 cm + 2 cm + 3 cm + 4 cm + 1 cm + 3 cm + 2 cm + 3 cm + 4 cm + 1 cm + 3 cm + 2 cm + 3 cm + 4 cm

= 52 cm

**Question 2. The lid of a rectangular box of sides 40 cm by 10 cm is sealed all around with tape. What is the length of the tape required?**

**Solution :**

Length of the tape required

= Perimeter of the rectangular box = 2 Ã— (Length + Breadth)

= 2 Ã— (40 cm + 10 cm)

= 2 Ã— (50 cm)

= 100 cm = l m.

**Question 3. A table-top measures 2 m 25 cm by l m 50 cm. What is the perimeter of the table-top?**

**Solution :**

The perimeter of the table-top

= 2 Ã— (Length + Breadth)

= 2 Ã— (2 m 25 cm + 1 m 50 cm)

= 2 Ã— (2.25 m+1.50 m)

= 2 Ã— (3.75 m)

= 7.5 m

**Question 4. What is the length of the wooden strip required to frame a photograph of length and breadth 32 cm and 21 cm respectively? **

**Solution :**

Length of the wooden strip required = 2 Ã— (Length + Breadth)

= 2 Ã— (32 cm + 21 cm)

= 2 Ã— (53 cm)

= 106 cm = 1.06 m.

**Question 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?**

**Solution :**

Perimeter of the rectangle

= 2 Ã— (Length + Breadth )

= 2 Ã— (0.7 km + 0.5 km)

= 2 Ã— (1.2km)

= 2.4 km

Length of the wire needed

= 4 Ã— Perimeter of the rectangle = 4 Ã— (2.4 km)

= 9.6 km.

**Question 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 a mi third side 6 cm.

**Solution :**

**(a)** Perimeter of the triangle = 3 cm + 4 cm + 5 cm = 12 cm**(b)** Perimeter of the equilateral triangle = 3 Ã— Length of a side = 3 Ã— (9 cm) = 27 cm**(c)** Perimeter of the isosceles triangle = 8 cm + 8 cm + 6 cm = 22 cm.

**Question 7. Find the perimeter of a triangle with sides measuring 10 cm, 14 cm, and 15 cm.**

**Solution :**

Perimeter of the triangle

= Sum of the lengths of its three sides

= 10 cm + 14 cm + 15 cm

= 39 cm.

**Question 8. Find the perimeter of a regular hexagon with each side measuring 8 m.**

**Solution :**

Perimeter of the regular hexagon

= 6 Ã— Length of a side

= 6 Ã— (8m)

= 48 m.

**Question 9. Find the side of the square whose perimeter is 20 m. **

**Solution :**

Perimeter of the square

= 4 Ã— Length of a side

â‡’ Length of one side

**Question 10. The perimeter of a regular pentagon is 100 cm. How long is its every side?**

**Solution :**

Perimeter of the regular pentagon = 5 Ã— Length of a side

â‡’ Length of one (each) side

**Question 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?

**Solution :**

**(a)** Perimeter of the square = 4 Ã— Length of a side

â‡’ Length of a side

**(b)** Perimeter of the equilateral triangle

= 3 Ã— Length of a side

â‡’ Length of a side

**(c)** Perimeter of the regular hexagon = 6 Ã— Length of a side.

â‡’ Length of a side

**Question 12. Two sides of a triangle are 12 cm and 14 cm. The perimeter of the triangle is 36 cm. What is the third side?**

**Solution :**

Perimeter of a triangle = Sum of the lengths of its three sides

â‡’ 36 cm = 12 cm + 14 cm + Length of the third side

â‡’ 36 cm = 26 cm + Length of the third side

â‡’ Length of the third side = 36 cm â€“ 26 cm = 10 cm.

**Question 13. Find the cost of fencing a square park of side 250 m at the rate of â‚¹ 20 per meter.**

**Solution :**

Perimeter of the square park = 4 Ã— Length of a side = 4 Ã— (250m)

= 1000 m

âˆ´ Cost of fencing the square park at the rate of?

20 per metre = â‚¹ 1000 Ã— 20

= â‚¹ 20,000

**Question 14. Find the cost of fencing a rectangular park of length 175 m and breadth 125 m at the rate of? 12 per meter.**

**Solution :**

Perimeter of the rectangular park = 2 Ã— (Length + Breadth)

= 2 Ã— (175m + 125 m)

= 2 Ã— (300 m)

= 600 m

Cost of fencing the rectangular park at the rate of ?

12 per metre = â‚¹ 600 Ã— 12

= â‚¹ 7200.

**Question 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?**

**Solution :**

Perimeter of the square park = 4 Ã— Length of a side = 4 Ã— (75 m)

= 300 m

Perimeter of the rectangular park

= 2 Ã— (Length + Breadth)

= 2 Ã— (60 m + 45 m)

= 2 Ã— (105 m)

= 210 m.

Since, the perimeter of the rectangular park is less than the perimeter of the square park, therefore. Bulbul covers less distance.

**Question 16. What is the perimeter of each of the following figures? What do you infer from the answers?**

**Solution :**

**(a)** Perimeter

= Sum of the lengths of all the sides

= 25 cm + 25 cm + 25 cm + 25 cm

= 100 cm.

**(b)** Perimeter

= Sum of the lengths of all the sides

= 40 cm + 10 cm + 40 cm + 10 cm

= 100 cm.

**(c)** Perimeter

= Sum of the lengths of all the sides

= 30 cm + 20 cm + 30 cm + 20 cm

= 100 cm.

**(d)** Perimeter

= Sum of the lengths of all the sides

= 30 cm + 40 cm + 30 cm

= 100 cm.

The inference from the answers. All the figures have the same perimeter.

**Question 17. Avneet buys 9 square paving slabs, each with a side of 12 m. He lays them in the form of a square.**

**(a)** What is the perimeter of his arrangement (Fig. i)?**(b)** 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)?**(c)** Which has a greater perimeter?**(d)** 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.)

**Solution :**

**(a)** Perimeter of his arrangement = 4 Ã— Length of one side

**(b)** Perimeter of her arrangement = Sum of the lengths of all the sides

**(c)** Cross has greater perimeter.**(d)** Yes ! there is a way of getting an even greater perimeter. It is shown below:

## NCERT Solutions for Class 6 Maths Chapter 10 Mensuration Ex 10.1 PDF

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