ANSWER KEY Class 6 – Ganita Prakash – CHAPTER 6 PERIMETER AND AREA

 

Answer Key & Explanations

Multiple Choice Questions

1. c) 20 cm

2. a) 4 m

3. a) 5 cm

4. c) 1500 m

5. a) 9 cm

6. c) 7 cm

7. b) 8 cm

8. c) 16 sq. m

9. b) 20 m

10. c) The square has a larger area

11. b) 6 cm

12. c) Splitting

13. a) ₹1250

14. b) A square with side 5 cm

15. a) The area of each rectangle is half the area of the square

16. c) 1 sq. unit

17. c) 24 cm

18. b) 72 sq. cm

19. b) Half the area of the parallelogram

20. c) Increase, decrease, or remain the same

Assertion & Reasoning Questions

1. a) Both A and R are true, and R is the correct explanation of A

2. b) Both A and R are true, but R is not the correct explanation of A

3. d) A is false but R is true

4. a) Both A and R are true, and R is the correct explanation of A

5. d) A is false but R is true

6. a) Both A and R are true, and R is the correct explanation of A

7. a) Both A and R are true, and R is the correct explanation of A

8. a) Both A and R are true, and R is the correct explanation of A

9. a) Both A and R are true, and R is the correct explanation of A

10. a) Both A and R are true, and R is the correct explanation of A

11. a) Both A and R are true, and R is the correct explanation of A

12. a) Both A and R are true, and R is the correct explanation of A

13. a) Both A and R are true, and R is the correct explanation of A

14. a) Both A and R are true, and R is the correct explanation of A

15. a) Both A and R are true, and R is the correct explanation of A

16. c) A is true but R is false

17. a) Both A and R are true, and R is the correct explanation of A

18. a) Both A and R are true, and R is the correct explanation of A

19. a) Both A and R are true, and R is the correct explanation of A

20. b) Both A and R are true, but R is not the correct explanation of A

True/False Questions

1. False

2. False

3. True

4. False

5. True

6. True

7. False

8. False

9. True

10. True

Short Answer Type I (Sample Answers)

1. Perimeter = 4 × 12.5 = 50 cm

2. Breadth = 400/25 = 16 m

3. Perimeter = 15+20+25=60 m, Distance=2×60=120 m

4. Side = 48/4 = 12 m

5. Area of rectangle=10×8=80 sq cm, Side of square=√80=4√5 cm, Perimeter=16√5 cm

6. Perimeter of rectangle=2(12+8)=40 cm, Side of square=40/4=10 cm

7. (Split figure and calculate area of parts)

8. Side=35/5=7 cm

9. Perimeter=1200/15=80 m, Side=80/4=20 m

10. 2(10+b)=30 ⇒ b=5 cm, Area=10×5=50 sq cm

Short Answer Type II (Sample Answers)

1. Let breadth=b, length=2b, Perimeter=2(2b+b)=6b=150 ⇒ b=25 m, l=50 m, Area=50×25=1250 sq m

2. Area of floor=6×4=24 sq m, Area of carpet=3×3=9 sq m, Uncarpted area=24-9=15 sq m

3. a) Side=60/4=15 cm, b) Side=60/6=10 cm

4. Area of land=10×8=80 sq m, Area of 4 beds=4×(1.5×1.5)=9 sq m, Remaining area=80-9=71 sq m

5. (Add all outer side lengths)

6. Draw 3×4 rectangle (P=14) and 2×6 rectangle (P=16)

7. Outer dimensions: l=8+4=12 m, b=5+4=9 m, Area total=12×9=108 sq m, Area room=8×5=40 sq m, Area verandah=108-40=68 sq m

8. Breadth=120/15=8 cm, Perimeter=2(15+8)=46 cm

9. Perimeter=2(180+110)=580 m, Total rope=4×580=2320 m, Cost=2320×5=₹11,600

10. Draw rectangle, show diagonal creates two equal-area triangles

Long Answer Type (Sample Answers)

1. a) Side=64/4=16 cm, Area=16²=256 sq cm
   b) Breadth=256/32=8 cm, Perimeter=2(32+8)=80 cm
   c) Square perimeter=64 cm, Rectangle perimeter=80 cm, Rectangle has larger perimeter

2. Outer dimensions: l=85+10=95 m, b=60+10=70 m, Area total=95×70=6650 sq m, Area park=85×60=5100 sq m, Area path=6650-5100=1550 sq m, Cost=(1550×250)/10=₹38,750

3. a) Definitions of perimeter and area
   b) Sides: 15 cm, 20 cm, 25 cm (right-angled), Area=½×15×20=150 sq cm

4. (Calculate based on specific figure)

5. a) Perimeter=2(12+8)=40 cm, Side of square=40/4=10 cm
   b) Side of hexagon=40/6=6.67 cm
   c) Regular hexagon encloses more area

6. a) Twice as big
   b) 10 times
   c) Different perimeters

7. a) ΔABC and ΔADC
   b) Area of ΔABC=½×10×6=30 sq cm, Area of rectangle=60 sq cm
   c) Perimeter=10+6+11.6=27.6 cm

8. Area of 4 walls=2×3×(12+9)=126 sq m, Area of openings= (2×1.5)+2(1.5×1)=6 sq m, Area to whitewash=126-6=120 sq m, Cost=120×5=₹600

9. a) Smallest P=12 units (3×3 square)
   b) Largest P=20 units (1×9 line)
   c) Arrangement affects perimeter significantly

10. (Calculate based on given plan dimensions)

Case-Based Questions (Sample Answers)

Case 1:

1. 2×(70+40)=220 m

2. Perimeter=2×(60+30)=180 m, Total distance=7×180=1260 m

3. Akshi distance=5×220=1100 m, Toshi ran longer by 160 m

4. Akshi finishes first

Case 2:

1. A and B; C and E

2. Twice as big

3. 10 times

4. No, perimeter depends on arrangement

Case 3:

1. 2×(230+160)=780 m

2. 3×780=2340 m

3. 2340×8=₹18,720

4. Rope for 2 rounds=1560 m, Cost=1560×8=₹12,480, Saved=₹6,240

Case 4:

1. 4 cm

2. 16 sq cm

3. Area = length × breadth

4. (Student creates puzzle)

Case 5:

1. Area floor=5×4=20 sq m, Area carpet=3×3=9 sq m, Uncarpted=11 sq m

2. Area tile=0.2×0.2=0.04 sq m

3. Tiles needed=11/0.04=275

4. Extra tiles=10% of 275=28, Total=275+28=303 tiles