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Solutions

Overview

Step-by-step NCERT solutions for Perimeter and Area (Chapter 6, NCERT Class 6 Mathematics) — every question and answer worked out in full, not just the final result. You can also read the Perimeter and Area textbook chapter.

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All 41 questions in Perimeter and Area are solved in the PDF. Here's what's inside, exercise by exercise:

6.1 Perimeter

  1. 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 = ?
  2. A rectangle having sidelengths 5 cm and 3 cm is made using a piece of wire. If the wire is straightened and then bent to form a square, what will be the length of a side of the square?
  3. 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.
  4. 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 metre?
  5. 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 of equal length?
  6. A farmer has a rectangular field having length 230 m and breadth 160 m. He wants to fence it with 3 rounds of rope as shown. What is the total length of rope needed?

Matha Pachchi! (Running Tracks)

  1. Find out the total distance Akshi has covered in 5 rounds. (Akshi runs along the outer rectangular track of length 70 m and breadth 40 m.)
  2. Find out the total distance Toshi has covered in 7 rounds. Who ran a longer distance? (Toshi runs along the inner rectangular track of length 60 m and breadth 30 m.)
  3. Think and mark the positions as directed— a. Mark 'A' at the point where Akshi will be after she ran 250 m. b. Mark 'B' at the point where Akshi will be after she ran 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 ran 250 m. e. Mark 'Y' at the point where Toshi will…

6.1 Perimeter — Straight and Diagonal Units

  1. Write the perimeters of the four figures shown on the dot grid in terms of straight (s) and diagonal (d) units. (The figures spell out letters using horizontal/vertical red lines and diagonal blue lines on a dot grid.)

6.1 Perimeter — Split and Rejoin

  1. A rectangular paper chit of dimension 6 cm × 4 cm is cut into two equal pieces (each 6 cm × 2 cm). Arrangement (a) has a perimeter of 28 cm. Find out the perimeter of each of the other arrangements (b), (c), and (d).
  2. Arrange the two pieces (each 6 cm × 2 cm) to form a figure with a perimeter of 22 cm.

6.2 Area

  1. The area of a rectangular garden 25 m long is 300 sq m. What is the width of the garden?
  2. 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?
  3. 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?
  4. By splitting the following figures into rectangles, find their areas (all measures are given in metres). a. A staircase-shaped figure (with dimensions 3, 1, 2, 2, 4, 4, 3 labelled). b. A frame-shaped figure (with dimensions 5, 3, 3, 2, 1, 1 labelled).

6.2 Area — Tangram

  1. Cut out the tangram pieces (A, B, C, D, E, F, G). Explore and figure out how many pieces have the same area.
  2. How many times bigger is Shape D as compared to Shape C? What is the relationship between Shapes C, D and E?
  3. Which shape has more area: Shape D or F? Give reasons for your answer.
  4. Which shape has more area: Shape F or G? Give reasons for your answer.
  5. What is the area of Shape A as compared to Shape G? Is it twice as big? Four times as big?
  6. Can you now figure out the area of the big square formed with all seven pieces in terms of the area of Shape C?
  7. 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.
  8. Are the perimeters of the square and the rectangle formed from these 7 pieces different or the same? Give an explanation for your answer.

6.2 Area — Grid Area Estimation

  1. Find the area of the four figures shown on the dot grid using the conventions: full square = 1 sq unit, more than half = 1 sq unit, exactly half = 1/2 sq unit, less than half = ignore.

6.3 Area of a Triangle — Grid Figures

  1. Find the areas of the figures (a), (b), (c), (d), (e) shown on the grid by dividing them into rectangles and triangles.

Making it 'More' or 'Less' — 9 Unit Squares

  1. Using 9 unit squares (arranged so each square shares at least one full side with another), what is the smallest perimeter possible?
  2. Using 9 unit squares, what is the largest perimeter possible?
  3. Make a figure with 9 unit squares having a perimeter of 18 units.
  4. 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?

Making it 'More' or 'Less' — House Plans

  1. Below is the house plan of Charan in a rectangular plot (total dimensions 35 ft × 30 ft). Some measurements are given: Master Bedroom (15 ft × 15 ft, Area = 225 sq ft), Toilet (5 ft × 10 ft), Kitchen (15 ft × 12 ft, Area = 180 sq ft), Small Bedroom (15 ft × ___ ft, Area = 180 sq ft). a. Find the missing measurements. b. Find out the area of his house.
  2. Find the missing dimensions and area of Sharan's home. The plan width is 42 ft. Given: Master Bedroom (12 ft × 15 ft, Area = 180 sq ft), Kitchen (18 ft × 10 ft, Area = 180 sq ft), Small Bedroom (12 ft × 10 ft), Utility (Area = 70 sq ft). a. Find the missing measurements. b. Find out the area of his house. Compare the areas and perimeters of Sharan's house and Charan's house.

Area Maze Puzzles

  1. In each figure, find the missing value of either the length of a side or the area of a region. a. A 2×2 grid of rectangles: top-left = 13 sq cm, top-right = 26 sq cm, bottom-left = 15 sq cm, bottom-right = ? sq cm. b. An L-shaped compound figure with two regions each labelled 10 sq cm and a top-right region = ? sq cm (with labels 3 cm and 2 cm). c. Three stacked rectangles (total left height 15…

6.3 Area of a Triangle

  1. 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.
  2. The area of a rectangular garden that is 50 m long is 1000 sq m. Find the width of the garden.
  3. 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.
  4. 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?
  5. 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.
  6. 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?
  7. 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.
  8. 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? 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…
Sample

Worked examples

3 questions from Perimeter and Area, solved step by step.

6.1 Perimeter

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 = ?

a. Perimeter of a rectangle = 2 × (length + breadth)

14 = 2 × (length + 2)

7 = length + 2

length = 7 − 2 = 5 cm

b. Perimeter of a square = 4 × side

20 = 4 × side

side = 20 ÷ 4 = 5 cm

c. Perimeter of a rectangle = 2 × (length + breadth)

12 = 2 × (3 + breadth)

6 = 3 + breadth

breadth = 6 − 3 = 3 m

Answer: a. length = 5 cm; b. side = 5 cm; c. breadth = 3 m

Matha Pachchi! (Running Tracks)

Find out the total distance Toshi has covered in 7 rounds. Who ran a longer distance? (Toshi runs along the inner rectangular track of length 60 m and breadth 30 m.)

Perimeter of Toshi's inner track = 2 × (60 + 30) = 2 × 90 = 180 m

Total distance in 7 rounds = 7 × 180 = 1260 m

Akshi ran 1100 m; Toshi ran 1260 m

Toshi ran the longer distance.

Answer: Toshi covered 1260 m; Toshi ran the longer distance

6.2 Area — Tangram

How many times bigger is Shape D as compared to Shape C? What is the relationship between Shapes C, D and E?

Shape D can be exactly covered using Shapes C and E together.

So area of D = area of C + area of E.

Since C and E have equal areas: area of D = 2 × area of C.

Shape D is twice as big as Shape C.

Answer: D is 2 times bigger than C; D = C + E (area of D equals area of C and E combined)

All 41 questions in Perimeter and Area are solved step by step in the Solutions PDF above.

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More NCERT Solutions for Class 6

Read the Perimeter and Area textbook chapter / PDF, or browse all NCERT Class 6 Mathematics solutions.

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