Area

Q: A rectangle is 3 cm tall and 5 cm wide. What is its area?

15 cm² — 3 × 5 = 15 cm². That is 15 squares of 1 cm² each.

Q: A square has sides of 6 cm. What is its area?

36 cm² — 6 × 6 = 36 cm². In a square, the height and the width are the same.

Q: A room is 4 m by 5 m. What is its area?

20 m² — 4 × 5 = 20 m². That is about the size of a good-sized living room.

Q: Land costs ¥150,000 per m². How much is a plot of 60 m²?

¥9,000,000 — ¥150,000 × 60 = ¥9,000,000. The price rises in step with the area.

Q: How do you find the area of an L-shape?

Split it into rectangles and add them up — Either split it into rectangles and add them up, or start from one big rectangle and subtract the missing part.

Where this is used

Land, rooms, fields — how much they cost depends on how much space they take up. Even an air conditioner is chosen by the size of the room it can cool. Area is the number that ties space to money and to how powerful something needs to be.

Key points

Area is just how many 1 cm² squares fit inside

A square that is 1 cm on every side covers an area of 1 cm². Area means how many of those little squares fit inside a shape. If a rectangle is 3 cm down and 5 cm across, 15 squares fit inside — so its area is 15 cm².

The formula just saves you from counting

Area of a rectangle = height × width. This formula exists so you can get the answer in one multiplication instead of counting the squares one at a time. Don't learn it by heart on its own — remember that you are really counting squares, and you will never forget it.

Split an awkward shape up, then add

An L-shape is easy once you cut it into two rectangles and add them together. You could also take one big rectangle and subtract the missing corner. Either way you get the same answer. Breaking a problem into simpler pieces like this is probably the single most useful idea grown-ups use at work.

More space, more money

Within the same neighbourhood, the price of land goes up roughly in step with its area. Twice the area, twice the price. That is why the graph below is a straight line.

How much land costs (in an area where 1 m² costs ¥150,000)

Check yourself 5questions

Tap an option to check

Q1 A rectangle is 3 cm tall and 5 cm wide. What is its area?

Q2 A square has sides of 6 cm. What is its area?

Q3 A room is 4 m by 5 m. What is its area?

Q4 Land costs ¥150,000 per m². How much is a plot of 60 m²?

Q5 How do you find the area of an L-shape?

Jobs that use this

Every job uses this. The ones below are just where it shows up most.

Real estate agent $65k

Farmer $45k

Architect $85k

Real estate agent$65k

They work out what a piece of land or a flat is worth from its area, then explain that price to their customers. If they can't compare places by the price per square metre, they end up recommending the overpriced one.

Maths used: AreaProportionsPrice per unit

Farmer$45k

From the area of a field they estimate how much seed to sow, how much fertiliser to use, and how big the harvest will be. Getting the area right is what decides that year's income.

Maths used: AreaMultiplicationProportions

Architect$85k

The area of each room, the area of the windows, the largest floor area allowed on a given plot of land. Get one of these legal area calculations wrong and the building simply cannot be built.

Maths used: AreaVolumeRatios

Where this is used

Key points

Check yourself 5questions

Jobs that use this

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