NCERT Solutions - Class 6 Mathematics
Chapter 6: Perimeter and Area
Page No. 132
Section 6.1 — Perimeter
Q1. Find the missing terms:[cite: 6]
a. Perimeter of a rectangle = 14 cm; breadth = 2 cm; length = ?[cite: 6]
b. Perimeter of a square = 20 cm; side length = ?[cite: 6]
c. Perimeter of a rectangle = 12 m; length = 3 m; breadth = ?[cite: 6]
a. Perimeter of a rectangle = 14 cm; breadth = 2 cm; length = ?[cite: 6]
b. Perimeter of a square = 20 cm; side length = ?[cite: 6]
c. Perimeter of a rectangle = 12 m; length = 3 m; breadth = ?[cite: 6]
Ans.
a. Length = 5 cm[cite: 6]
b. Length of a side = 5 cm[cite: 6]
c. Breadth = 3 cm[cite: 6]
a. Length = 5 cm[cite: 6]
b. Length of a side = 5 cm[cite: 6]
c. Breadth = 3 cm[cite: 6]
Q2. A rectangle having side lengths 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?[cite: 6]
Ans. Length of a side of square = 4 cm[cite: 6]
Q3. 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?[cite: 6]
Ans. Length of the third side of triangle = 21 cm[cite: 6]
Q4. What would be the cost of fencing a rectangular park whose length is 150 m and breadth is 120 m, if the fence costs Rs. 40 per metre?[cite: 6]
Ans. Perimeter = 2 × (150 + 120) = 540 m[cite: 6]
Cost = 540 × 40 = Rs. 21,600[cite: 6]
Cost = 540 × 40 = Rs. 21,600[cite: 6]
Q5. A piece of string is 36 cm long. What will be the length of each side, if it is used to form:[cite: 6]
a. A square,[cite: 6]
b. A triangle with all sides of equal length, and[cite: 6]
c. A hexagon (a six-sided closed figure) with sides of equal length?[cite: 6]
a. A square,[cite: 6]
b. A triangle with all sides of equal length, and[cite: 6]
c. A hexagon (a six-sided closed figure) with sides of equal length?[cite: 6]
Ans.
a. Length of each side of square = 9 cm[cite: 6]
b. Length of each side of regular triangle = 12 cm[cite: 6]
c. Length of each side of regular hexagon = 6 cm[cite: 6]
a. Length of each side of square = 9 cm[cite: 6]
b. Length of each side of regular triangle = 12 cm[cite: 6]
c. Length of each side of regular hexagon = 6 cm[cite: 6]
Q6. A farmer has a rectangular field having length 230 m and breadth 160 m. He wants to fence it with 3 rounds of rope. What is the total length of rope needed?[cite: 6]
Ans.
Perimeter of the field = 780 m[cite: 6]
Total length of the rope needed = 2340 m[cite: 6]
Perimeter of the field = 780 m[cite: 6]
Total length of the rope needed = 2340 m[cite: 6]
Page No. 133
Q1. Find out the total distance Akshi has covered in 5 rounds.[cite: 6]
Ans.
Perimeter of the outer track = 220 m[cite: 6]
Total distance covered in 5 rounds = 1100 m[cite: 6]
Perimeter of the outer track = 220 m[cite: 6]
Total distance covered in 5 rounds = 1100 m[cite: 6]
Q2. Find out the total distance Toshi has covered in 7 rounds. Who ran a longer distance?[cite: 6]
Ans.
Perimeter of the inner track = 180 m[cite: 6]
Total distance covered in 7 rounds = 1260 m[cite: 6]
Toshi ran a longer distance.[cite: 6]
Perimeter of the inner track = 180 m[cite: 6]
Total distance covered in 7 rounds = 1260 m[cite: 6]
Toshi ran a longer distance.[cite: 6]
Page No. 134
Deep Dive
Deep Dive Q. Distance from Point A and Point B to the finishing flag.[cite: 6]
Ans.
• From point A to flag: 100 + 100 + 100 + 50 = 350 m[cite: 6]
• From point B to flag: 125 + 150 + 75 = 350 m[cite: 6]
• From point A to flag: 100 + 100 + 100 + 50 = 350 m[cite: 6]
• From point B to flag: 125 + 150 + 75 = 350 m[cite: 6]
Q. Akshi says that the perimeter of this triangle shape is 9 units. Toshi says it can't be 9 units and the perimeter will be more than 9 units. What do you think?[cite: 6]
Ans. The perimeter will be more than 9 units as the length of a diagonal of a square is always greater than the sides of the square.[cite: 6]
Page No. 135
Q. Write the perimeters of the figures in terms of straight (s) and diagonal (d) units.[cite: 6]
Ans. The perimeters of the figures: 8s + 2d, 4s + 6d, 12s + 6d, 18s + 6d.[cite: 6]
Q. Generalise your understanding for the perimeter of regular polygons.[cite: 6]
Ans. In general, Perimeter of regular polygon = Number of sides × Length of a side.[cite: 6]
Page No. 138
Section 6.2 — Area
Q1. The area of a rectangular garden 25 m long is 300 sq m. What is the width of the garden?[cite: 6]
Ans. Width = 300 ÷ 25 = 12 m[cite: 6]
Q2. What is the cost of tiling a rectangular plot of land 500 m long and 200 m wide at the rate of Rs. 8 per hundred sq. m?[cite: 6]
Ans. Cost of tiling = Rs. 8000[cite: 6]
Q3. 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?[cite: 6]
Ans. 200 trees.[cite: 6]
Q4. By splitting the following figures into rectangles, find their areas:[cite: 6]
a. Figure (a)[cite: 6]
b. Figure (b)[cite: 6]
a. Figure (a)[cite: 6]
b. Figure (b)[cite: 6]
Ans.
(a) 28 sq. m[cite: 6]
(b) 9 sq. m[cite: 6]
(a) 28 sq. m[cite: 6]
(b) 9 sq. m[cite: 6]
Page No. 140
Q. Find the area of the following figures.[cite: 6]
Ans. 4 sq. units, 9 sq. units, 10 sq. units, 11 sq. units.[cite: 6]
Page No. 144 - 145
Section 6.3 — Area and Perimeter Exploration
Q1. Find the areas of the figures below by dividing them into rectangles.[cite: 6]
Ans.
a. 24 sq. units[cite: 6]
b. 30 sq. units[cite: 6]
c. 48 sq. units[cite: 6]
d. 16 sq. units[cite: 6]
e. 12 sq. units[cite: 6]
a. 24 sq. units[cite: 6]
b. 30 sq. units[cite: 6]
c. 48 sq. units[cite: 6]
d. 16 sq. units[cite: 6]
e. 12 sq. units[cite: 6]
Q. Using 9 unit squares, solve the following:[cite: 6]
1. What is the smallest perimeter possible?[cite: 6]
2. What is the largest perimeter possible?[cite: 6]
3. Make a figure with a perimeter of 18 units.[cite: 6]
4. Can you make other shaped figures for each perimeter?[cite: 6]
1. What is the smallest perimeter possible?[cite: 6]
2. What is the largest perimeter possible?[cite: 6]
3. Make a figure with a perimeter of 18 units.[cite: 6]
4. Can you make other shaped figures for each perimeter?[cite: 6]
Ans.
1. Smallest perimeter = 12 cm (obtained from a square of side 3 cm)[cite: 6]
2. Largest perimeter = 20 cm (obtained from a rectangle of length 9 cm and breadth 1 cm)[cite: 6]
4. Yes, except for the smallest perimeter.[cite: 6]
1. Smallest perimeter = 12 cm (obtained from a square of side 3 cm)[cite: 6]
2. Largest perimeter = 20 cm (obtained from a rectangle of length 9 cm and breadth 1 cm)[cite: 6]
4. Yes, except for the smallest perimeter.[cite: 6]
Page No. 146 - 147
Q. Charan's House Plan Area & Dimensions[cite: 6]
| Room / Area | Dimensions | Area |
|---|---|---|
| Small Bedroom | 15 ft × 12 ft | 180 sq ft |
| Utility | 15 ft × 3 ft | 45 sq ft |
| Hall | 20 ft × 12 ft | 240 sq ft |
| Parking | 15 ft × 3 ft | 45 sq ft |
| Garden | 20 ft × 3 ft | 60 sq ft |
Q. Sharan's House Plan Area & Comparison[cite: 6]
| Room / Area | Dimensions | Area |
|---|---|---|
| Utility | 7 ft × 10 ft | 70 sq ft |
| Hall | 23 ft × 15 ft | 345 sq ft |
| Entrance | 7 ft × 15 ft | 105 sq ft |
| Small Bedroom | 12 ft × 10 ft | 120 sq ft |
| Toilet | 5 ft × 10 ft | 50 sq ft |
• Area of Sharan's house: 42 ft × 25 ft = 1050 sq ft[cite: 6]
• Area Comparison: Both houses have equal areas (1050 sq ft).[cite: 6]
• Perimeter Comparison: Charan's house = 130 ft; Sharan's house = 134 ft.[cite: 6] The perimeter of Sharan's house is greater.[cite: 6]
Page No. 148
Q. Area Maze Puzzles[cite: 6]
Ans.
a. 30 sq cm[cite: 6]
b. 9 sq cm[cite: 6]
c. 16 sq cm[cite: 6]
d. 5 cm[cite: 6]
a. 30 sq cm[cite: 6]
b. 9 sq cm[cite: 6]
c. 16 sq cm[cite: 6]
d. 5 cm[cite: 6]
Page No. 149
Q1. Give the dimensions of a rectangle whose area is the sum of the areas of two rectangles: 5 m × 10 m and 2 m × 7 m.[cite: 6]
Ans. Total Area = 50 + 14 = 64 sq m. Possible dimensions: 16 m × 4 m, 32 m × 2 m, or 8 m × 8 m.[cite: 6]
Q2. The area of a rectangular garden that is 50 m long is 1000 sq m. Find the width of the garden?[cite: 6]
Ans. 20 m.[cite: 6]
Q3. The floor of a room is 5 m long and 4 m wide. A square carpet whose sides are 3 m is laid on the floor. Find the area that is not carpeted.[cite: 6]
Ans. Area not carpeted = 11 sq m.[cite: 6]
Q4. Four flower beds (2 m × 1 m) are dug at four corners of a garden (15 m × 12 m). How much area is available for laying down a lawn?[cite: 6]
Ans. Available area = 172 sq m.[cite: 6]
Q5. Shape A has area 18 sq units; Shape B has area 20 sq units. Shape A has a longer perimeter than Shape B. Draw two such shapes.[cite: 6]
Ans. Possible dimensions: Shape A (2m × 9m, Perimeter = 22m), Shape B (5m × 4m, Perimeter = 18m). Here, P(A) > P(B).[cite: 6]
Q7. Outer rectangle: 12 units × 8 units. Draw an inner rectangle with exactly half the area.[cite: 6]
Ans. Area of outer rectangle = 96 sq units. Area of inner rectangle = 48 sq units.[cite: 6]
Q8. A square piece of paper is folded in half and cut into two rectangles. Which statement is always true?[cite: 6]
Ans. Statement C is true: The perimeters of both rectangles added together is always 1.5 times the perimeter of the square.[cite: 6]
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