CBSE Important Questions Class 6 Maths Chapter 6 – Perimeter and Area

Class 6 Maths Chapter 6 Perimeter and Area is part of the new NCERT textbook Ganita Prakash. It teaches students how to find the distance around a shape (its perimeter) and the space a shape covers (its area). Students learn the perimeter of rectangles, squares, triangles and regular polygons, how to find area by counting unit squares, the area of rectangles and squares, and how the area of a triangle is half the area of a rectangle drawn around it.

These CBSE important questions for Class 6 Maths Chapter 6 cover multiple choice questions, area on a grid, comparing perimeter and area, and real-life word problems such as running around a park, fencing a garden, tiling a floor and framing a photograph. Every question has a clear step-by-step answer in simple English, so students can practise on their own, parents can check the working, and teachers can use them for class tests. A free printable PDF of these important questions is also available on this page.

CBSE Important Questions Class 6 Maths Chapter 6 – Perimeter and Area

Perimeter and Area (New NCERT)
Medium
Q.
​Find the missing terms:
(a) Perimeter of a rectangle = 14 cm; breadth = 2 cm; length = ?
(b) Perimeter of a square = 20 cm; side of a length = ?
(c) Perimeter of a rectangle = 12 m; length = 3 m; breadth = ?​
Perimeter and Area (New NCERT)
Medium
Q.
​Find various objects from your surroundings that have regular shapes and find their perimeters. Also, generalize your understanding of the perimeter of other regular polygons.​
Perimeter and Area (New NCERT)
Medium
Q.
​Four flower beds having sides 2 m long and 1 m wide are dug at the four corners of a garden that is 15 m long and 12 m wide. How much area is now available for laying down a lawn?​
Perimeter and Area (New NCERT)
Medium
Q.
​Shape A has an area of 18 square units and Shape B has an area of 20 square units. Shape A has a longer perimeter than Shape B. Draw two such shapes satisfying the given conditions.​
Perimeter and Area (New NCERT)
Medium
Q.
On a page in your book, draw a rectangular border that is 1 cm from the top and bottom and 1.5 cm from the left and right sides. What is the perimeter of the border?
Perimeter and Area (New NCERT)
Medium
Q.
​Draw a rectangle of size 12 units × 8 units. Draw another rectangle inside it, without touching the outer rectangle that occupies exactly half the area.​
Perimeter and Area (New NCERT)
Medium
Q.
A square piece of paper is folded in half. The square is then cut into two rectangles along the fold. Regardless of the size of the square, one of the following statements is always true. Which statement is true here?
​(a) The area of each rectangle is larger than the area of the square.
(b) The perimeter of the square is greater than the perimeters of both the rectangles added together.
(c) The perimeters of both the rectangles added together are always 112 \frac{1}{2}\;​times the perimeter of the square.
(d) The area of the square is always three times as large as the areas of both rectangles added together.​
Perimeter and Area (New NCERT)
Medium
Q.
Akshi and Toshi start running along the rectangular tracks as shown in the figure. Akshi runs along the outer track and completes 5 rounds. Toshi runs along the inner track and completes 7 rounds. Now, they are wondering who ran more. Find out who ran the longer distance.
​
Perimeter and Area (New NCERT)
Medium
Q.
In races, usually, there is a common finish line for all the runners. Here are two square running tracks with an inner track of 100 m on each side and an outer track of 150 m on each side. The common finishing line for both runners is shown by the flags in the figure which are in the center of one of the sides of the tracks. If the total race is 350 m, then we have to find out where the starting positions of the two runners should be on these two tracks so that they both have a common finishing line after they run for 350 m. Mark the starting points of the runner on the inner track as ‘A ’ and the runner on the outer track as ‘B’.
Perimeter and Area (New NCERT)
Medium
Q.
A rectangular paper chit of dimension 6 cm × 4 cm is cut as shown into two equal pieces. These two pieces are joined in different ways.
For example, the arrangement a. has a perimeter of 28 cm.
Find out the length of the boundary (i.e., the perimeter) of each of the other arrangements below.
Perimeter and Area (New NCERT)
Medium
Q.
​The area of a rectangular garden that is 50 m long is 1000 sq m. Find the width of the garden.​
Perimeter and Area (New NCERT)
Medium
Q.
​Arrange the two pieces to form a figure with a perimeter of 22 cm.​

Perimeter and Area (New NCERT)
Medium
Q.
Find the area of the following figures. 
Perimeter and Area (New NCERT)
Medium
Q.
On a squared grid paper (1 square = 1 square unit), make as many rectangles as you can whose lengths and widths are a whole number of units such that the area of the rectangle is 12 square units.
(a) Which rectangle has the greatest perimeter?
(b) Which rectangle has the least perimeter?
(c) If you take a rectangle of area 32 sq cm, what will your answers be? Given any area, is it possible to predict the shape of the rectangle with the greatest perimeter as well as the least perimeter? Give examples and reasons for your answer
Perimeter and Area (New NCERT)
Medium
Q.
Draw a rectangle on a piece of paper and draw one of its diagonals. Cut the rectangle along that diagonal and get two triangles.
Check! whether the two triangles overlap each other exactly. Do they have the same area?​
​Can you draw any inferences from this exercise? Please write it here.​​
Perimeter and Area (New NCERT)
Medium
Q.
Use your understanding from previous grades to calculate the area of any closed figure using grid paper and-
​1. Find the area of the blue triangle BAD.
2. Find the area of the red triangle ABE.​
Perimeter and Area (New NCERT)
Medium
Q.
Using 9 unit squares, what is the smallest perimeter possible?
Perimeter and Area (New NCERT)
Medium
Q.
Using 9 unit squares, what is the largest perimeter possible?
Perimeter and Area (New NCERT)
Medium
Q.
​Make a figure with a perimeter of 18 units.​
Perimeter and Area (New NCERT)
Medium
Q.
The floor of a room is 5 m long and 4 m wide. A square carpet whose sides are 3 m in length is laid on the floor. Find the area that is not carpeted.
Perimeter and Area (New NCERT)
Medium
Q.
​Give the dimensions of a rectangle whose area is the sum of the areas of these two rectangles having measurements: 5 m × 10 m and 2 m × 7 m.​
Perimeter and Area (New NCERT)
Medium
Q.
A rectangle with sidelengths 5 cm and 3 cm is made using a wire. If the wire is straightened and then bent to form a square, what will be the length of the side of the square?
Perimeter and Area (New NCERT)
Medium
Q.
What is the cost of tiling a rectangular plot of land 500 m long and 200 m wide at the rate of ₹ 8 per hundred sq m?
Perimeter and Area (New NCERT)
Medium
Q.
​Find the length of the third side of a triangle having a perimeter of 55 cm and having two sides of length 20 cm and 14 cm, respectively.​
Perimeter and Area (New NCERT)
Medium
Q.
​What would be the cost of fencing a rectangular park whose length is 150 m and breadth is 120 m if the fence costs ₹ 40 per meter?​
Perimeter and Area (New NCERT)
Medium
Q.
A piece of string is 36 cm long. What will be the length of each side, if it is used to form:
(a) A square,
(b) A triangle with all sides of equal length, and
(c) A hexagon (a six-sided closed figure) with sides oil equal length?
Perimeter and Area (New NCERT)
Medium
Q.
A farmer has a rectangular field with having length of 230 m and a breadth of 160 m. He wants to fence it with 3 rounds of rope as shown. What is the total length of rope needed?
Perimeter and Area (New NCERT)
Medium
Q.
​Find out the total distance Akshi has covered in 5 rounds.​
Perimeter and Area (New NCERT)
Medium
Q.
Find out the total distance Toshi has covered in 7 rounds. Who ran a longer distance?​
Perimeter and Area (New NCERT)
Medium
Q.
Think and mark the positions as directed-
(a) Mark ‘A’ at the point where Akshi will be after she runs 250 m.
(b) Mark ‘B’ at the point where Akshi will be after she runs 500 m.
(c) Now, Akshi ran 1000 m. How many full rounds has she finished running around her track? Mark her position as ‘C
(d) Mark ‘X’ at the point where Toshi will be after she runs 250 m.
(e) Mark ‘Y’ at the point where Toshi will be after she runs 500 m.
(f) Now, Toshi ran 1000 m. How many full rounds has she finished running around her track? Mark her position as ‘Z’.
Perimeter and Area (New NCERT)
Medium
Q.
​The area of a rectangular garden 25 m long is 300 sq m. What is the width of the garden?​
Perimeter and Area (New NCERT)
Medium
Q.
​A rectangular coconut grove is 100 m long and 50 m wide. If each coconut tree requires 25 sq m, what is the maximum number of trees that can be planted in this grove?​
Perimeter and Area (New NCERT)
Medium
Q.
​Find the areas of the figures below by dividing them into rectangles and triangles.
Perimeter and Area (New NCERT)
Medium
Q.
By splitting the following figures into rectangles, find their areas (all measures are given in meters):
Perimeter and Area (New NCERT)
Medium
Q.
​Explore and figure out how many pieces have the same area.​
Perimeter and Area (New NCERT)
Medium
Q.
​How many times bigger is Shape D as compared to Shape C? What is the relationship between Shapes C, D, and E?​
Perimeter and Area (New NCERT)
Medium
Q.
​Which shape has more area: Shape D or F? Give reasons for your answer.​
Perimeter and Area (New NCERT)
Medium
Q.
​Which shape has more area: Shape F or G? Give reasons for your answer.​
Perimeter and Area (New NCERT)
Medium
Q.
What is the area of Shape A as compared to Shape G? Is it twice as big? Four times as big?
[Hint: In the tangram pieces, by placing the shapes over each other, we can find out that Shapes A and B have the same area, and Shapes C and E have the same area. You would have also figured out that Shape D can be exactly covered using Shapes C and E, which means Shape D has twice the area of Shape C or Shape E, etc.]
Perimeter and Area (New NCERT)
Medium
Q.
Arrange these 7 pieces to form a rectangle. What will be the area of this rectangle in terms of the area of Shape C now? Give reasons for your answer.
Perimeter and Area (New NCERT)
Medium
Q.
​Are the perimeters of the square and the rectangle formed from these 7 pieces different or the same? Give an explanation for your answer.​
Perimeter and Area (New NCERT)
Medium
Q.
​Can you make other shaped figures for each of the above three perimeters, or is there only one shape with that perimeter? What is your reasoning?​

CBSE Important Questions Class 6 Maths Chapter 6 – Perimeter and Area

Q1. What is the perimeter of a rectangle whose length is 12 cm and breadth is 8 cm?
(a) 20 cm
(b) 40 cm
(c) 96 cm
(d) 48 cm

Answer: (b) 40 cm
Perimeter of a rectangle = 2 × (length + breadth)
= 2 × (12 cm + 8 cm) = 2 × 20 cm = 40 cm

Q2. The side of a square is 9 m. What is its area?
(a) 36 sq m
(b) 18 sq m
(c) 81 sq m
(d) 81 m

Answer: (c) 81 sq m
Area of a square = side × side = 9 m × 9 m = 81 sq m.
Area is always written in square units, so option (d) 81 m is not correct.

Q3. Each side of an equilateral triangle is 7 cm. What is its perimeter?
(a) 14 cm
(b) 21 cm
(c) 49 cm
(d) 28 cm

Answer: (b) 21 cm
An equilateral triangle has three equal sides.
Perimeter = 3 × side = 3 × 7 cm = 21 cm

Q4. The perimeter of a square park is 64 m. What is the length of each side?
(a) 8 m
(b) 32 m
(c) 16 m
(d) 256 m

Answer: (c) 16 m
Perimeter of a square = 4 × side
So, side = perimeter ÷ 4 = 64 m ÷ 4 = 16 m

Q5. Find the area of the shape drawn on the grid. Each small square is 1 square unit.
(a) 10 square units
(b) 11 square units
(c) 12 square units
(d) 13 square units

Shape of a house drawn on a grid with 10 full squares and 2 half squares

Answer: (b) 11 square units
Count the full squares: the body of the house has 3 × 3 = 9 squares, and there is 1 more square in the roof. So there are 10 full squares.
The roof also has 2 half squares (the triangles). 2 half squares = 1 full square.
Area = 10 + 1 = 11 square units

Q6. Look at rectangles A (6 cm × 4 cm) and B (8 cm × 3 cm). Which statement is true?
(a) They have the same area and the same perimeter
(b) They have the same area but different perimeters
(c) They have different areas but the same perimeter
(d) They have different areas and different perimeters

Rectangle A of 6 cm by 4 cm and rectangle B of 8 cm by 3 cm drawn on a grid

Answer: (b) They have the same area but different perimeters
Area of A = 6 × 4 = 24 sq cm; Area of B = 8 × 3 = 24 sq cm. The areas are equal.
Perimeter of A = 2 × (6 + 4) = 20 cm; Perimeter of B = 2 × (8 + 3) = 22 cm. The perimeters are different.
So shapes with the same area can have different perimeters.

Q7. Triangle PQR is drawn on a grid of unit squares. What is its area?
(a) 24 square units
(b) 12 square units
(c) 10 square units
(d) 20 square units

Right triangle PQR on a grid, shown as half of a 6 by 4 rectangle

Answer: (b) 12 square units
The dotted lines complete a rectangle of 6 units × 4 units around the triangle.
Area of the rectangle = 6 × 4 = 24 square units.
The diagonal PR cuts the rectangle into two equal triangles, so the area of triangle PQR = 24 ÷ 2 = 12 square units.

Q8. A regular hexagon has each side 5 cm long. What is its perimeter?
(a) 25 cm
(b) 30 cm
(c) 35 cm
(d) 20 cm

Answer: (b) 30 cm
A regular hexagon has 6 equal sides.
Perimeter = 6 × side = 6 × 5 cm = 30 cm

Q9. Meera takes 3 rounds of a rectangular park that is 80 m long and 45 m wide. How much distance does she cover?

Rectangular park 80 m long and 45 m wide with a running path around it

Answer: Meera covers 750 m.
Distance covered in 1 round = perimeter of the park
= 2 × (80 m + 45 m) = 2 × 125 m = 250 m
Distance covered in 3 rounds = 3 × 250 m = 750 m

Q10. A square garden has a side of 25 m. Find the cost of fencing it all around at the rate of ₹40 per metre.

Answer: The cost of fencing is ₹4,000.
Length of fence needed = perimeter of the garden = 4 × 25 m = 100 m
Cost of fencing = 100 × ₹40 = ₹4,000

Q11. The area of a rectangle is 96 sq cm and its length is 12 cm. Find its breadth and perimeter.

Answer: Breadth = 8 cm; Perimeter = 40 cm
Area = length × breadth ⇒ 96 = 12 × breadth
Breadth = 96 ÷ 12 = 8 cm
Perimeter = 2 × (12 cm + 8 cm) = 2 × 20 cm = 40 cm

Q12. A room floor is 6 m long and 4 m wide. It is to be covered with square tiles of side 50 cm. How many tiles are needed? If each tile costs ₹45, find the total cost of the tiles.

Answer: 96 tiles are needed and the total cost is ₹4,320.
Side of each tile = 50 cm = 0.5 m
Tiles along the length = 6 m ÷ 0.5 m = 12; tiles along the width = 4 m ÷ 0.5 m = 8
Number of tiles = 12 × 8 = 96
(Check: area of floor = 6 × 4 = 24 sq m; area of one tile = 0.5 × 0.5 = 0.25 sq m; 24 ÷ 0.25 = 96)
Total cost = 96 × ₹45 = ₹4,320

Floor of 6 m by 4 m covered with 12 by 8 square tiles of side 50 cm

Q13. A wire 36 cm long is bent to form a square. The same wire is then straightened and bent to form a rectangle of length 12 cm. Which shape encloses more area, and by how much?

Answer: The square encloses more area, by 9 sq cm.
The perimeter of both shapes is equal to the length of the wire, 36 cm.
Square: side = 36 ÷ 4 = 9 cm; area = 9 × 9 = 81 sq cm
Rectangle: 2 × (12 + breadth) = 36 ⇒ 12 + breadth = 18 ⇒ breadth = 6 cm; area = 12 × 6 = 72 sq cm
Difference = 81 − 72 = 9 sq cm

A 36 cm wire bent into a 9 cm square and a 12 cm by 6 cm rectangle

Q14. Draw all the rectangles with whole-number sides (in cm) that have a perimeter of 20 cm. Which of them has the greatest area?

Answer: The 5 cm × 5 cm square has the greatest area (25 sq cm).
Perimeter = 2 × (length + breadth) = 20 cm, so length + breadth = 10 cm.
Possible sides: 9 × 1, 8 × 2, 7 × 3, 6 × 4 and 5 × 5
Their areas: 9, 16, 21, 24 and 25 sq cm
All five have the same perimeter, but the area grows as the sides become closer to each other. The square has the greatest area.

Rectangles 9 by 1, 8 by 2, 7 by 3, 6 by 4 and 5 by 5 with perimeter 20 cm and their areas

Q15. A photograph 20 cm long and 15 cm wide is pasted on a card, leaving a border of 2 cm all around it. Find (i) the length and width of the card, (ii) the area of the border.

Answer: (i) 24 cm × 19 cm (ii) 156 sq cm
(i) The border adds 2 cm on each side. Length of card = 20 + 2 + 2 = 24 cm; width of card = 15 + 2 + 2 = 19 cm
(ii) Area of card = 24 × 19 = 456 sq cm; area of photograph = 20 × 15 = 300 sq cm
Area of border = 456 − 300 = 156 sq cm

Photograph of 20 cm by 15 cm on a 24 cm by 19 cm card with a 2 cm border

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