NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 6: Mensuration

Problems and Solutions

Four regular hexagons are drawn so as to form the design as shown in Fig. 6.11. 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 10 m long and 4 m 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 1 m for the entrance. Find the length of fencing.

The region given in Fig. 6.13 is measured by taking one small square 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 Fig. 6.14. Their sides are 4 cm, 10 cm and 3 cm. 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 250 m and width is 150 m. Anuradha runs around this field 3 times. How far did she run? How many times should she 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 each side?

The perimeter of a triangle is 28 cm. One of its sides is 8 cm. 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.

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 1 m 50 cm and breadth 1 m. There is a 100 m 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 Fig. 6.16? 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 Fig. 6.17 is Rs 55000. Find the cost of fencing per metre.

In Fig. 6.18 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 are shown)
• (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 15 cm length (Fig. 6.19). Find the area of the wall.

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

Anmol has chart paper 90×40 cm, Abhishek has 50×70 cm. Which covers more area and by how much?

A rectangular path 60 m × 3 m is covered by tiles of 25 cm side. Find number of tiles.

How many square slabs of side 90 cm are needed to cover floor of area 81 sq m?

Rectangular field length 8 m, breadth 2 m. Square field has same perimeter. Find which has greater area.

Parmindar walks once around a square park and covers 800 m. Find area of park.

Side of square = 5 cm. How many times does area increase if side is doubled?

Rectangular cards 8×5 cm are cut from square chart 60 cm side. How many cards? What area left?

Magazine charges Rs 300 per 10 sq cm. Half page ad size 15×24 ÷ 2. Find cost.

Perimeter of square = 48 m. Small bed covers 18 sq m. Find area not covered, fraction, and ratio.

Perimeter of square and rectangle same. Square side = 15 cm, rectangle one side = 18 cm. Find rectangle area.

Wire bent into small squares of side 2 cm. Total area = 28 cm². Find original length of wire.

Divide park of Fig. 6.17 into rectangles. Total area? Fertilizer per 300 sqm, how many packets?

Rectangular field area = 1600 sqm, length = 80 m. Find perimeter.

Area of each square on chess board = 4 sq cm. Find total area.

• (a) Area left unoccupied.
• (b) Area occupied.

(a) Find all rectangles with perimeter 36 cm. (b) Find all with area 36 sq cm.

Find area and perimeter of figures in Fig. 6.20 if each square = 1 sq cm.

Each square area? Whole figure area=96. Find perimeter. (Fig. 6.21)