Areas in real life

Start with something on your desk. An A4 sheet is 21 cm by 29.7 cm, so its area is 21 × 29.7 = 623.7 cm². Picture how many A4 sheets would cover your table, and you have estimated its area without a measuring tape.

Furniture is often measured in inches and feet. The conversions are 1 in = 2.54 cm and 1 ft = 12 in. So 5 in = 12.7 cm, and 7.4 in = 18.796 cm. The other way: 5.08 cm = 2 in and 11.43 cm = 4.5 in.

Converting areas is where people slip. How many cm² are in 1 in²? A square of side 1 in is a square of side 2.54 cm, so its area is 2.54 × 2.54 = 6.4516 cm², not 2.54. The length factor gets squared, because both sides are converted.

So 10 in² = 10 × 6.4516 = 64.516 cm². And backwards: every 6.4516 cm² makes one in², so 161.29 cm² = 161.29 ÷ 6.4516 = 25 in².

The same squaring rule works all the way up. 1 ft = 12 in, so 1 ft² = 12 × 12 = 144 in². And 1 km = 1000 m, so 1 km² = 1000 × 1000 = 1,000,000 m².

Rooms and houses are usually measured in ft² or m². Land is often measured in acres, where 1 acre = 43,560 ft². Towns and cities are measured in km².

India also has many local units of area still in daily use: bigha, gaj, katha, dhur, cent, ankanam and others, which differ from state to state. Find out which one is used where you live, and what it equals in m².

Then estimate. What is the area of your classroom? Your school? Your town? How many times bigger is your town than your school? Look up which city has the largest area in India and in the world, and which has the smallest. The answers are often surprising, because area and population are not the same thing at all.