Area — Class 8 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 8 Mathematics chapter "Area" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 8 Mathematics chapter "Area" — 8 important questions with detailed answers for CBSE board exam preparation…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
NCERT Solutions for Class 8 Mathematics — Area. Step-by-step answers to all 8 textbook questions from this chapter, written for CBSE board preparation and free to use.
Area — All 8 Questions Solved
Q1. Find the area of a rectangle with length 8 cm and width 5 cm.
Step 1: Area of rectangle = length × width
Step 2: Area = 8 × 5 = 40 cm²
Q2. Find the area of a triangle with base 12 cm and height 8 cm.
Step 1: Area of triangle = (1/2) × base × height
Step 2: Area = (1/2) × 12 × 8
Step 3: Area = (1/2) × 96 = 48 cm²
Q3. Calculate the circumference and area of a circle with radius 7 cm.
Step 1: Circumference = 2πr = 2 × π × 7 = 14π cm
Step 2: Circumference ≈ 14 × 3.14 = 43.96 cm
Step 3: Area = πr² = π × 7² = 49π cm²
Step 4: Area ≈ 49 × 3.14 = 153.86 cm²
Q4. Find the area of a trapezoid with parallel sides 6 cm and 10 cm, and height 5 cm.
Step 1: Area of trapezoid = (1/2) × (sum of parallel sides) × height
Step 2: Area = (1/2) × (6 + 10) × 5
Step 3: Area = (1/2) × 16 × 5
Step 4: Area = (1/2) × 80 = 40 cm²
Q5. Find the surface area of a cube with side 4 cm.
Step 1: A cube has 6 equal square faces.
Step 2: Area of one face = side² = 4² = 16 cm²
Step 3: Surface area = 6 × 16 = 96 cm²
Q6. Find the volume of a rectangular prism with length 10 cm, width 6 cm, and height 5 cm.
Step 1: Volume = length × width × height
Step 2: Volume = 10 × 6 × 5 = 300 cm³
Q7. Find the perimeter of a square with side 9 cm.
Step 1: A square has 4 equal sides.
Step 2: Perimeter = 4 × side
Step 3: Perimeter = 4 × 9 = 36 cm
Q8. Find the volume of a cylinder with radius 3 cm and height 10 cm.
Step 1: Volume of cylinder = πr²h
Step 2: Volume = π × 3² × 10
Step 3: Volume = π × 9 × 10 = 90π cm³
Step 4: Volume ≈ 90 × 3.14 = 282.6 cm³
Area — Practice MCQs with Answers
Attempt these 20 multiple-choice questions after working through the solutions above. Each carries the correct option and the reasoning behind it, so a wrong answer tells you which idea to revisit.
MCQ 1. The side of a square park is 30 meters. What is its area?
- A. 90 m²
- B. 120 m²
- C. 900 m²
- D. 60 m²
Answer: C. 900 m² — The area of a square is calculated by the formula side × side. So, 30 m × 30 m = 900 m².
MCQ 2. A rectangular field is 80 meters long and 40 meters wide. Find its area.
- A. 320 m²
- B. 120 m²
- C. 240 m²
- D. 3200 m²
Answer: D. 3200 m² — The area of a rectangle is calculated by the formula length × width. So, 80 m × 40 m = 3200 m².
MCQ 3. What is the area of a triangle with a base of 10 cm and a height of 6 cm?
- A. 30 cm²
- B. 60 cm²
- C. 16 cm²
- D. 20 cm²
Answer: A. 30 cm² — The area of a triangle is calculated by the formula (1/2) × base × height. So, (1/2) × 10 cm × 6 cm = 30 cm².
MCQ 4. A parallelogram has a base of 12 cm and a corresponding height of 7 cm. Find its area.
- A. 84 cm²
- B. 42 cm²
- C. 19 cm²
- D. 72 cm²
Answer: A. 84 cm² — The area of a parallelogram is calculated by the formula base × height. So, 12 cm × 7 cm = 84 cm².
MCQ 5. If the area of a square plot is 144 square meters, what is the length of its side?
- A. 10 m
- B. 12 m
- C. 14 m
- D. 16 m
Answer: B. 12 m — The area of a square is side². To find the side, take the square root of the area. √144 m² = 12 m.
MCQ 6. The area of a rectangular hall is 150 m². If its length is 15 m, what is its breadth?
- A. 10 m
- B. 20 m
- C. 12 m
- D. 15 m
Answer: A. 10 m — The area of a rectangle is length × breadth. Given area = 150 m² and length = 15 m, so breadth = Area / length = 150 m² / 15 m = 10 m.
MCQ 7. Find the area of a rhombus whose diagonals are 16 cm and 12 cm.
- A. 96 cm²
- B. 192 cm²
- C. 48 cm²
- D. 28 cm²
Answer: A. 96 cm² — The area of a rhombus is calculated by the formula (1/2) × d1 × d2, where d1 and d2 are the lengths of the diagonals. So, (1/2) × 16 cm × 12 cm = 96 cm².
MCQ 8. The parallel sides of a trapezium are 10 cm and 14 cm, and its height is 5 cm. Calculate its area.
- A. 60 cm²
- B. 30 cm²
- C. 120 cm²
- D. 70 cm²
Answer: A. 60 cm² — The area of a trapezium is calculated by the formula (1/2) × (sum of parallel sides) × height. So, (1/2) × (10 cm + 14 cm) × 5 cm = (1/2) × 24 cm × 5 cm = 60 cm².
MCQ 9. A circular garden has a radius of 7 meters. What is its area? (Use π = 22/7)
- A. 44 m²
- B. 154 m²
- C. 22 m²
- D. 14 m²
Answer: B. 154 m² — The area of a circle is calculated by the formula πr². So, (22/7) × 7 m × 7 m = 22 × 7 m² = 154 m².
MCQ 10. How many square centimeters are there in 1 square meter?
- A. 100 cm²
- B. 1000 cm²
- C. 10000 cm²
- D. 100000 cm²
Answer: C. 10000 cm² — Since 1 meter = 100 centimeters, 1 square meter = 1 m × 1 m = 100 cm × 100 cm = 10000 cm².
MCQ 11. A path 1 meter wide is built along the border inside a square garden of side 30 meters. What is the area of the path?
- A. 116 m²
- B. 120 m²
- C. 124 m²
- D. 112 m²
Answer: A. 116 m² — The area of the outer square is 30m × 30m = 900 m². The inner square has a side of 30m - 2m (path on both sides) = 28m, so its area is 28m × 28m = 784 m². The area of the path is the difference: 900 m² - 784 m² = 116 m².
MCQ 12. The area of a triangular field is 48 m². If its base is 12 m, what is its height?
- A. 8 m
- B. 6 m
- C. 4 m
- D. 10 m
Answer: A. 8 m — The area of a triangle is (1/2) × base × height. Given area = 48 m² and base = 12 m, so 48 = (1/2) × 12 × height. This simplifies to 48 = 6 × height, so height = 48 / 6 = 8 m.
MCQ 13. The circumference of a circle is 88 cm. What is its radius? (Use π = 22/7)
- A. 7 cm
- B. 14 cm
- C. 21 cm
- D. 28 cm
Answer: B. 14 cm — The circumference of a circle is 2πr. Given circumference = 88 cm, so 88 = 2 × (22/7) × r. This simplifies to 88 = (44/7) × r, so r = 88 × (7/44) = 2 × 7 = 14 cm.
MCQ 14. The area of a rhombus is 100 cm². If one of its diagonals is 20 cm, what is the length of the other diagonal?
- A. 5 cm
- B. 10 cm
- C. 15 cm
- D. 20 cm
Answer: B. 10 cm — The area of a rhombus is (1/2) × d1 × d2. Given area = 100 cm² and d1 = 20 cm, so 100 = (1/2) × 20 × d2. This simplifies to 100 = 10 × d2, so d2 = 100 / 10 = 10 cm.
MCQ 15. A field in the form of a trapezium has an area of 340 m². The length of its parallel sides are 30 m and 20 m. Find the perpendicular distance between them.
- A. 10 m
- B. 12 m
- C. 14 m
- D. 13.6 m
Answer: D. 13.6 m — The area of a trapezium is (1/2) × (sum of parallel sides) × height. Given area = 340 m², sum of parallel sides = 30m + 20m = 50m. So, 340 = (1/2) × 50 × height. This simplifies to 340 = 25 × height, so height = 340 / 25 = 13.6 m.
MCQ 16. If the length of a rectangle is increased by 20% and its breadth is decreased by 10%, what is the percentage change in its area?
- A. 8% increase
- B. 8% decrease
- C. 10% increase
- D. 10% decrease
Answer: A. 8% increase — Let original length be L and breadth be B. Original Area = LB. New length = L + 0.20L = 1.2L. New breadth = B - 0.10B = 0.9B. New Area = 1.2L × 0.9B = 1.08LB. Percentage change = ((1.08LB - LB) / LB) × 100 = 0.08 × 100 = 8% increase.
MCQ 17. A rectangular lawn is 50 m long and 40 m wide. A path of width 2 m is to be built around the lawn (outside). Find the area of the path.
- A. 384 m²
- B. 360 m²
- C. 376 m²
- D. 392 m²
Answer: C. 376 m² — The outer length of the lawn including the path will be 50 + 2 + 2 = 54 m, and outer breadth will be 40 + 2 + 2 = 44 m. The area of the outer rectangle is 54 × 44 = 2376 m². The area of the lawn is 50 × 40 = 2000 m². The area of the path is 2376 - 2000 = 376 m².
MCQ 18. What is the area of a semi-circle whose diameter is 14 cm? (Use π = 22/7)
- A. 77 cm²
- B. 154 cm²
- C. 38.5 cm²
- D. 22 cm²
Answer: A. 77 cm² — The radius of the semi-circle is half of the diameter, so r = 14 cm / 2 = 7 cm. The area of a full circle is πr², which is (22/7) × 7² = 154 cm². The area of a semi-circle is half of the full circle's area, so 154 / 2 = 77 cm².
MCQ 19. How many hectares are there in a field of 50,000 m²? (1 hectare = 10,000 m²)
- A. 5 hectares
- B. 0.5 hectares
- C. 50 hectares
- D. 500 hectares
Answer: A. 5 hectares — Since 1 hectare = 10,000 m², to convert square meters to hectares, divide by 10,000. So, 50,000 m² / 10,000 = 5 hectares.
MCQ 20. A square and a rectangle have the same perimeter. If the side of the square is 16 cm and the rectangle has a length of 18 cm, what is the area of the rectangle?
- A. 256 cm²
- B. 288 cm²
- C. 252 cm²
- D. 264 cm²
Answer: C. 252 cm² — Perimeter of square = 4 × side = 4 × 16 cm = 64 cm. Since the rectangle has the same perimeter, 2(length + breadth) = 64 cm. Given length = 18 cm, so 2(18 + breadth) = 64. 36 + 2 × breadth = 64. 2 × breadth = 28. Breadth = 14 cm. Area of rectangle = length × breadth = 18 cm × 14 cm = 252 cm².
How to Use These Solutions
Attempt each question yourself first and only then compare with the worked answer. Marks in the CBSE board exam are awarded for the METHOD as much as the final result, so reproduce the steps rather than memorising the last line. Where a solution states a law, a formula or a definition, learn that wording — examiners look for it.
Related practice for this chapter: chapter MCQs, previous-year questions, revision notes and sample papers.