#### Chapters

## Chapter 6: Mensuration

### NCERT solutions for Mathematics Exemplar Class 6 Chapter 6 Mensuration Exercise [Pages 93 - 102]

#### Choose the correct alternative:

Following figures are formed by joining six unit squares. Which figure has the smallest perimeter in figure?

A square shaped park ABCD of side 100m has two equal rectangular flower beds each of size 10m × 5m (Figure). Length of the boundary of the remaining park is ______.

360 m

400 m

340 m

460 m

The side of a square is 10 cm. How many times will the new perimeter become if the side of the square is doubled?

2 times

4 times

6 times

8 times

Length and breadth of a rectangular sheet of paper are 20 cm and 10 cm, respectively. A rectangular piece is cut from the sheet as shown in figure. Which of the following statements is correct for the remaining sheet?

Perimeter remains same but area changes

Area remains the same but perimeter changes

Both area and perimeter are changing

Both area and perimeter remain the same

Two regular Hexagons of perimeter 30 cm each are joined as shown in figure. The perimeter of the new figure is ______.

65 cm

60 cm

55 cm

50 cm

In figure which of the following is a regular polygon? All have equal side except (i).

#### Match the shapes (each sides measures 2cm) in column I with the corresponding perimeters in column II:

Column I |
Column II |

(A) | (i) 16 cm |

(B) | (ii) 20 cm |

(C) | (iii) 24 cm |

(D) | (iv) 28 cm |

(v) 32 cm |

#### Match the following:

Shapes |
Perimeter |

(A) | (i) 10 |

(B) | (ii) 18 |

(C) | (iii) 20 |

(D) | (iv) 25 |

#### Fill in the blank:

Perimeter of the shaded portion in the given figure is ______.

AB + _ + _ + _ + _ + _ + _ + HA

The amount of region enclosed by a plane closed figure is called its ______.

Area of a rectangle with length 5 cm and breadth 3 cm is ______.

A rectangle and a square have the same perimeter (Figure).

**(a)** The area of the rectangle is ______.

**(b)** The area of the square is ______.

1 m = ______ cm.

1 sq cm = ______ cm × 1 cm.

1 sq m = 1 m × ______ m = 100 cm × ______ cm.

1 sq m = ______ sq cm.

#### State whether the following statement is True or False:

If length of a rectangle is halved and breadth is doubled then the area of the rectangle obtained remains same.

True

False

Area of a square is doubled if the side of the square is doubled.

True

False

Perimeter of a regular octagon of side 6 cm is 36 cm.

True

False

A farmer who wants to fence his field, must find the perimeter of the field.

True

False

An engineer who plans to build a compound wall on all sides of a house must find the area of the compound.

True

False

To find the cost of painting a wall we need to find the perimeter of the wall.

True

False

To find the cost of a frame of a picture, we need to find the perimeter of the picture.

True

False

Four regular hexagons are drawn so as to form the design as shown in the given figure. If the perimeter of the design is 28 cm, find the length of each side of the hexagon.

Perimeter of an isosceles triangle is 50 cm. If one of the two equal sides is 18 cm, find the third side.

Length of a rectangle is three times its breadth. Perimeter of the rectangle is 40 cm. Find its length and width.

There is a rectangular lawn 10m long and 4m wide in front of Meena’s house (see the figure). It is fenced along the two smaller sides and one longer side leaving a gap of 1m for the entrance. Find the length of fencing.

The region given in the following figure is measured by taking as a unit. What is the area of the region?

Tahir measured the distance around a square field as 200 rods (lathi). Later he found that the length of this rod was 140 cm. Find the side of this field in metres.

The length of a rectangular field is twice its breadth. Jamal jogged around it four times and covered a distance of 6 km. What is the length of the field?

Three squares are joined together as shown in figure. Their sides are 4 cm, 10 cm and 3 cm. Find the perimeter of the figure.

In the given figure, all triangles are equilateral and AB = 8 units. Other triangles have been formed by taking the mid points of the sides. What is the perimeter of the figure?

Length of a rectangular field is 250 m and width is 150 m. Anuradha runs around this field 3 times. How far did she run? How many times she should run around the field to cover a distance of 4 km?

Bajinder runs ten times around a square track and covers 4 km. Find the length of the track.

The lawn in front of Molly’s house is 12 m × 8 m, whereas the lawn in front of Dolly’s house is 15 m × 5 m. A bamboo fencing is built around both the lawns. How much fencing is required for both?

The perimeter of a regular pentagon is 1540 cm. How long is its each side?

The perimeter of a triangle is 28 cm. One of it’s sides is 8cm. Write all the sides of the possible isosceles triangles with these measurements.

The length of an aluminium strip is 40 cm. If the lengths in cm are measured in natural numbers, write the measurement of all the possible rectangular frames which can be made out of it. (For example, a rectangular frame with 15 cm length and 5 cm breadth can be made from this strip.)

Base of a tent is a regular hexagon of perimeter 60 cm. What is the length of each side of the base?

In an exhibition hall, there are 24 display boards each of length 1m 50 cm and breadth 1 m. There is a 100m long aluminium strip, which is used to frame these boards. How many boards will be framed using this strip? Find also the length of the aluminium strip required for the remaining boards.

In the above question, how many square metres of cloth is required to cover all the display boards? What will be the length in m of the cloth used, if its breadth is 120 cm?

What is the length of outer boundary of the park shown in the given figure? What will be the total cost of fencing it at the rate of Rs 20 per metre? There is a rectangular flower bed in the center of the park. Find the cost of manuring the flower bed at the rate of Rs 50 per square metre.

Total cost of fencing the park shown in the given figure is Rs 55000. Find the cost of fencing per metre.

In the given figure, each square is of unit length**(a)** What is the perimeter of the rectangle ABCD? **(b)** What is the area of the rectangle ABCD? **(c)** Divide this rectangle into ten parts of equal area by shading squares. (Two parts of equal area are shown here)**(d)** Find the perimeter of each part which you have divided. Are they all equal?

Rectangular wall MNOP of a kitchen is covered with square tiles of 15cm length (see figure)). Find the area of the wall.

Length of a rectangular field is 6 times its breadth. If the length of the field is 120 cm, find the breadth and perimeter of the field.

Anmol has a chart paper of measure 90 cm × 40 cm, whereas Abhishek has one which measures 50 cm × 70 cm. Which will cover more area on the table and by how much?

A rectangular path of 60 m length and 3 m width is covered by square tiles of side 25 cm. How many tiles will there be in one row along its width? How many such rows will be there? Find the number of tiles used to make this path?

How many square slabs each with side 90cm are needed to cover a floor of area 81 sq m.

The length of a rectangular field is 8 m and breadth is 2 m. If a square field has the same perimeter as this rectangular field, find which field has the greater area.

Parmindar walks around a square park once and covers 800 m. What will be the area of this park?

The side of a square is 5 cm. How many times does the area increase, if the side of the square is doubled?

Amita wants to make rectangular cards measuring 8 cm × 5 cm. She has a square chart paper of side 60 cm. How many complete cards can she make from this chart? What area of the chart paper will be left?

A magazine charges Rs 300 per 10 sq cm area for advertising. A company decided to order a half page advertisment. If each page of the magazine is 15 cm × 24 cm, what amount will the company has to pay for it?

The perimeter of a square garden is 48 m. A small flower bed covers 18 sq m area inside this garden. What is the area of the garden that is not covered by the flower bed? What fractional part of the garden is covered by flower bed? Find the ratio of the area covered by the flower bed and the remaining area.

Perimeter of a square and a rectangle is same. If a side of the square is 15 cm and one side of the rectangle is 18 cm, find the area of the rectangle.

A wire is cut into several small pieces. Each of the small pieces is bent into a square of side 2 cm. If the total area of the small squares is 28 square cm, what was the original length of the wire?

Divide the park shown in the figure of question 40 into two rectangles. Find the total area of this park. If one packet of fertilizer is used for 300 sq m, how many packets of fertilizer are required for the whole park?

The area of a rectangular field is 1600 sq m. If the length of the field is 80 m, find the perimeter of the field.

The area of each square on a chess board is 4sqcm. Find the area of the board.**(a)** At the beginning of game when all the chess men are put on the board, write area of the squares left unoccupied. **(b)** Find the area of the squares occupied by chess men.

Find all the possible dimensions (in natural numbers) of a rectangle with a perimeter 36 cm and find their areas.

Find all the possible dimensions (in natural numbers) of a rectangle with an area of 36 sq cm, and find their perimeters.

Find the area and Perimeter of the following figure, if area of small square is 1 sq cm.

Find the area and perimeter of the following figure, if area of small square is 1 sq cm.

Find the area and perimeter of the following figure, if area of small square is 1 sq cm.

What is the area of each small square in the given figure. if the area of entire figure is 96 sq cm. Find the perimeter of the figure.

## Chapter 6: Mensuration

## NCERT solutions for Mathematics Exemplar Class 6 chapter 6 - Mensuration

NCERT solutions for Mathematics Exemplar Class 6 chapter 6 (Mensuration) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Exemplar Class 6 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics Exemplar Class 6 chapter 6 Mensuration are Mensuration, Concept of Perimeter, Perimeter of a Rectangle, Perimeter of Squares, Perimeter of Triangles, Perimeter of Polygon, Concept of Area, Area of Rectangle, Area of Square.

Using NCERT Class 6 solutions Mensuration exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 6 prefer NCERT Textbook Solutions to score more in exam.

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