Ncert exemplar solutions mathematics class 6 Solutions for Chapter 6 mensuration

In questions 1 to 6, out of the four options only one is correct. Write the correct answer.

Following figures are formed by joining six unit squares. Which figure has the smallest perimeter in Fig. 6.4?

A square shaped park ABCD of side 100m has two equal rectangular flower beds each of size 10m × 5m (Fig. 6.5). Length of the boundary of the remaining park is

(A) 360m (B) 400m (C) 340m (D) 460m

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

(A) 2 times (B) 4 times (C) 6 times (D) 8 times

Length and breadth of a rectangular sheet of paper are 20cm and 10cm, respectively. A rectangular piece is cut from the sheet as shown in Fig. 6.6. Which of the following statements is correct for the remaining sheet?

(A) Perimeter remains same but area changes.

(B) Area remains the same but perimeter changes.

(C) Both area and perimeter are changing.

(D) Both area and perimeter remain the same.

Two regular Hexagons of perimeter 30cm each are joined as shown in Fig. 6.7. The perimeter of the new figure is

(A) 65cm (B) 60cm (C) 55cm (D) 50cm

In Fig. 6.8 which of the following is a regular polygon? All have equal side except (i)

(A) (i) (B) (ii) (C) (iii)

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

Match the following

In questions 9 to 13, fill in the blanks to make the statements true.

Perimeter of the shaded portion in Fig. 6.9 is

AB + + + + + + + HA

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

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

A rectangle and a square have the same perimeter (Fig. 6.10).

(a) The area of the rectangle is _________

(b) The area of the square is _________

(a) 1m = _________ cm.

(b) 1sqcm = _________ cm × 1cm.

(c) 1sqm = 1m × _________ m = 100cm × _________ cm.

(d) 1sqm = _________ sqcm.

In questions 14 to 20, state which of the statements are true and which are false.

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

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

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

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

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

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

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

Four regular hexagons are drawn so as to form the design as shown in Fig. 6.11. If the perimeter of the design is 28cm, find the length of each side of the hexagon.

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

There is a rectangular lawn 10m long and 4m wide in front of Meena’s house (Fig. 6.12). 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.

Tahir measured the distance around a square field as 200 rods (lathi). Later he found that the length of this rod was 140cm. 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 6km. What is the length of the field?

Three squares are joined together as shown in Fig. 6.14. Their sides are 4cm, 10cm and 3cm. Find the perimeter of the figure.

In Fig. 6.15 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 250m and width is 150m. 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 4km?