Project: measure your room

Your room, your numbers

Today no new topic. Today you take a tape measure, paper and a pencil — and you work out your own room. Everything you learned in Fraction kid, at once and for real.

What the project will check:

• Measuring and decimal numbers: the sizes of the room will come out in metres with a point (3.6 m — lesson three in action).
• Area: how many m² does the floor have? How much carpet would you buy? (Lesson nineteen.)
• Surface area: how many m² of walls would be painted? (Twenty-one.)
• Volume: how much air is in the room? (Twenty-two + units from twenty-three.)
• A plan with coordinates: you draw furniture on a grid. (Twenty-six.)

Work like a craftsperson: measure twice, write at once, count with an estimate. A real room is not a textbook cuboid — it has windows, a door and a radiator. You can handle that too: subtracting areas you already can.

You need: a tape measure (or a tailor’s tape), paper, a pencil. Ideally a partner to hold the tape — a parent, a sibling.

Filip’s parents are planning painting and Filip offered: “I’ll count how much paint to buy.” He measured the room: 3.6 × 3.0 m, height 2.5 m. Walls: two of 3.6 × 2.5 and two of 3.0 × 2.5 — together 33 m². “Minus the window and the door,” he mutters, “that is about 3 m²… 30 left.” On the tin it says: 1 litre for 6 m², it will be painted twice. “Sixty square metres divided by six — ten litres.” Dad in the shop counts again on a calculator and gets the same. “Good work, engineer.” Filip’s numbers saved a return trip for a second tin.

Working method of the project

Phase 1: Measure and write (5 minutes). Length and width of the room along the floor, height from the floor to the ceiling. Write in metres with a decimal point (357 cm = 3.57 m — the point two places to the left). Measure the window and the door too (width × height).

Phase 2: Floor (area). S = length × width. It comes out in m². That is also the area of the ceiling and the area of carpet, if it were laid.

Phase 3: Walls (surface area without floor and ceiling). Two walls length × height, two walls width × height — add. From the result subtract the window and the door (you work out their areas the same: width × height). The rest is the painted area.

Phase 4: Air (volume). V = length × width × height. It comes out in m³. For interest: 1 m³ of air weighs about 1.2 kg — how many kilos of air do you have in the room?

Phase 5: A plan in coordinates. On squared paper draw axes, 1 little square = half a metre (write the scale!). The outline of the room, then furniture as rectangles — write the coordinates of each corner.

By every result write a unit (m, m², m³) and a sense check: a child’s room floor is usually 8–20 m², height around 2.5 m, volume 20–50 m³. A number outside those bounds = measure again.

Sample room: floor and carpet

A room 3.6 m × 3.0 m.

Floor: S = 3.6 × 3.0 = 10.8 m² (decimal multiplying: 36 × 30 = 1080, two decimal places back → 10.80).

Carpet is sold in whole m² — I round up: 11 m².

A sense check: 10.8 m² is a normal child’s room (between 8 and 20) ✓. And the perimeter for skirting: 2 × (3.6 + 3.0) = 13.2 m.

Sample room: walls minus window and door

Height 2.5 m. Walls:

• 2 × (3.6 × 2.5) = 2 × 9 = 18 m²
• 2 × (3.0 × 2.5) = 2 × 7.5 = 15 m²
• Together 33 m².

Window 1.5 × 1.2 = 1.8 m². Door 0.8 × 2.0 = 1.6 m². I subtract: 33 − 1.8 − 1.6 = 29.6 m² to paint.

For two coats: 59.2 m². At 6 m² per litre: 59.2 : 6 ≈ 9.9 → buy 10 litres.

Sample room: volume and a plan

Volume: V = 3.6 × 3.0 × 2.5. In steps: 3.6 × 3.0 = 10.8, then 10.8 × 2.5 = 27 m³.

That is 27 000 litres of air (the bridge from lesson 23) — and it weighs about 27 × 1.2 ≈ 32 kg. The air in the room weighs like a proper dog!

Plan: axes on squared paper, 1 little square = 0.5 m. The room is a rectangle [0; 0] to [7.2; 6] little squares… rounded corner [0;0], [7;0], [7;6], [0;6]. A bed 2 × 1 m = a rectangle 4 × 2 little squares, for example from [0; 0] to [4; 2].

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. 시작 with ten. When it goes well, add more.

Practise the area of a rectangle — in the project you count it for the floor and every wall. The answer is a number (in cm²).

Practise the questions

Project step by step

This is your big output from Fraction kid. Do it properly — keep the finished sheet with numbers.

1. Measure the room (length, width, height) and the window with the door. Write everything in metres with a decimal point in a clear table.

2. Work out: area of the floor (m²), perimeter of the floor (m), area of the walls without window and door (m²) and volume of the room (m³). By each result a unit and a short sense check.

3. Work out a shop: carpet for the floor (whole m², up) and paint for two coats of walls (coverage 6 m² per litre, up to whole litres).

4. Draw a plan of the room on a coordinate grid (1 little square = 0.5 m) and mark at least three pieces of furniture. Write the corners of one of them as coordinates.

Now you 💪

1. I have a table of sizes in metres with decimal points — no mixed units.
2. I have four results with the right units: m, m², m² and m³.
3. My plan has axes, a scale and furniture that can be written with coordinates.

What to take from this lesson

• Real measuring gives decimal numbers — and you can count with them.
• Floor = area (m²), walls = areas minus windows and doors, air = volume (m³).
• Round shop buys up: carpet to whole m², paint to whole litres.
• Before multiplying, unify the units. Always.
• A plan with a scale and coordinates is the language architects speak.

© 2026 Ing. Martin Polak / AlgoRhino · 콘텐츠 이용 약관