Q1.
How many cm² is 10 in²?
Answer
10 in² = 10 × 6.4516 cm²
= 64.516 cm²
= 64.516 cm²
Tip: 10 in² is not a square of side 10 in — that would be 100 in². It is any region whose area happens to be ten square inches.
NCERT Solutions Ganita Prakash (Part 2) Chapter 7 Areas in Real Life — In-text Questions
Book page 171 Updated on2026-09-05
Q2.
Convert 161.29 cm² to in². Evaluate the quotient.
Answer
Every 6.4516 cm² makes one square inch, so divide.
161.29 cm² = 161.29 ÷ 6.4516 in²
= 25 in²
= 25 in²
Check it yourself: 25 × 6.4516 = 161.29 ✓ — and 25 in² is exactly a square of side 5 in, whose side in centimetres is 5 × 2.54 = 12.7 cm, giving 12.7² = 161.29 cm². ✓
Q3.
What do you think is the area of your classroom?
Answer
Pace out the length and the breadth, then multiply. For a typical classroom of 8 m by 6 m:
Area = 8 × 6 = 48 m²
In square feet, since 1 m ≈ 3.28 ft:
48 m² ≈ 48 × 3.28² ≈ 48 × 10.76 ≈ 516 ft²
Tip: one normal step is roughly 0.75 m, so counting steps along two walls gives a quick estimate without a measuring tape.
Q4.
How many in² is 1 ft²?
Answer
1 ft = 12 in
1 ft² = (12 in) × (12 in) = 12² in²
= 144 in²
1 ft² = (12 in) × (12 in) = 12² in²
= 144 in²
Why it happens: again the area factor is the square of the length factor. A square foot is a 12 by 12 array of square inches — the same reason a square metre is 100 × 100 = 10,000 cm².
Q5.
What do you think is the area of your school? Make an estimate and compare it with the actual data.
Answer
Estimate first, then check against the school's records or a satellite map.
A school with 20 classrooms of about 48 m² each, plus corridors, offices, an assembly area and a playground, might work out like this:
Built-up area ≈ 20 × 48 = 960 m², plus about half as much again for corridors and rooms ≈ 1500 m²
Playground ≈ 70 m × 50 m = 3500 m²
Total ≈ 5000 m² = 0.005 km²
Playground ≈ 70 m × 50 m = 3500 m²
Total ≈ 5000 m² = 0.005 km²
That is roughly 1.2 acres (since 1 acre = 43,560 ft² ≈ 4047 m²).
Try This: compare your estimate with the school's registered plot area. Being within 20% of the true figure is a good estimate.
Q6.
Find out the local unit of area measurement in your region.
Answer
Ask a farmer, a shopkeeper or the local land records office. Different parts of India use very different units, and even the same name can mean different sizes in different districts.
| Unit | Mainly used in | Roughly equal to |
|---|---|---|
| bigha | UP, Bihar, Bengal, Rajasthan, Assam | varies widely — about 1500 to 2500 m² |
| katha (kattha) | Bihar, Bengal, Assam | 1/20 of a bigha |
| dhur | Bihar, Nepal border districts | 1/20 of a katha |
| gaj (square yard) | north India, for house plots | about 0.836 m² |
| cent | Kerala, Tamil Nadu | 1/100 acre ≈ 40.5 m² |
| ankanam | Andhra Pradesh, Karnataka | about 6 to 8 m² |
| guntha | Maharashtra, Karnataka | about 101 m² |
Why it happens: these units grew out of farming — how much land a pair of bullocks could plough in a day, or how much seed it took to sow. Because soils and practices differ from place to place, a bigha in Bengal is not a bigha in Rajasthan. That is exactly why standard units like m² and hectares were introduced for official records.
Q7.
What do you think is the area of your village/town/city? Make an estimate and compare it with the actual data.
Answer
Estimate by fitting a rectangle around the settlement on a map, then look up the official figure from the panchayat, municipality or census.
A town stretching about 6 km by 4 km:
Area ≈ 6 × 4 = 24 km²
1 km² = 1000 m × 1000 m = 10,00,000 m²
so 24 km² = 2,40,00,000 m²
Area ≈ 6 × 4 = 24 km²
1 km² = 1000 m × 1000 m = 10,00,000 m²
so 24 km² = 2,40,00,000 m²
Tip: a settlement is never a neat rectangle, so a rectangle drawn around it always overestimates. Halving the rectangle's area often gives a better guess for an irregularly spread town.
Q8.
How many m² is a km²?
Answer
1 km = 1000 m
1 km² = (1000 m) × (1000 m)
= 1000² m²
= 10,00,000 m² (ten lakh square metres)
1 km² = (1000 m) × (1000 m)
= 1000² m²
= 10,00,000 m² (ten lakh square metres)
Why it happens: length is multiplied by 1000, so area is multiplied by 1000² = 10,00,000. It is easy to guess "1000" by mistake — remember that a square kilometre holds a thousand rows of a thousand square metres each.
Did you know? 1 hectare = 10,000 m², so 1 km² = 100 hectares ≈ 247 acres.
Q9.
How many times is your village/town/city bigger than your school?
Answer
Divide the two areas — after writing both in the same unit.
Town ≈ 24 km² = 2,40,00,000 m²
School ≈ 5000 m²
2,40,00,000 ÷ 5000 = 4800 times
School ≈ 5000 m²
2,40,00,000 ÷ 5000 = 4800 times
So about 4800 schools of that size would fill the town.
Tip: never divide 24 by 0.005 without first checking that both numbers are in km². Comparing a number in km² with a number in m² is the commonest mistake in questions like this.
Q10.
Find the city with the largest area in (i) India, and (ii) the world.
Answer
The answer depends on what counts as "the city" — the area governed by the municipal corporation, or the whole built-up urban sprawl around it. Look up current figures, because municipal boundaries are redrawn quite often.
- (i) India. By area under a single municipal body, the largest are usually reported as Delhi (the NCT covers about 1,484 km², of which the municipal area is a large part) and Bengaluru (BBMP, about 700–800 km²). Mumbai's municipal area, by contrast, is only about 440 km² — yet it holds far more people.
- (ii) The world. Chongqing in China is usually named the largest, at roughly 82,000 km² — but that is an administrative region the size of a small country, most of it countryside. By continuously built-up urban area, New York and Tokyo are near the top, at a few thousand km² each.
Check it yourself: compare each city's area with its population to get the population density (people per km²). Delhi's large area and Mumbai's small one make their densities very different, which is the more useful number.
Q11.
Find the city with the smallest area in (i) India, and (ii) the world.
Answer
This is harder to pin down than the largest, because there is no agreed cut-off for when a town becomes a city.
- (i) India. Among municipal corporations, some of the smallest cover only a few square kilometres — for example small hill towns and cantonment towns of about 5–15 km². Your state's Directorate of Municipal Administration publishes the exact figures.
- (ii) The world. Vatican City is the smallest independent state at about 0.44 km² — smaller than many school playgrounds put together, and small enough to walk across in a few minutes.
0.44 km² = 0.44 × 10,00,000 = 4,40,000 m²
Try This: compare 0.44 km² with the area of your own school. If your school covers 5000 m², then Vatican City is only about 88 times as big.