Home / Teaching / 3r ESO / Challenges / 04 · Renovating our first flat
3r ESO · Maths challenges Notes 25 Sep 2026

Renovating our first flat

Revising 2n ESO: working out how much paint, parquet and skirting board a flat renovation needs, and what it costs. Each task has its solution hidden underneath.

Download the problem sheet (PDF, in Catalan) Formula sheet (PDF, in Catalan)

The situation

Imagine you are moving into your first flat. You want it to be a cosy place to live with your friends and family, so you need to do some renovation work:

  • Paint the walls of the living room and of one bedroom.
  • Lay parquet on the living-room floor.
  • Fit a wooden skirting board all round the living room.

Your budget is limited, so you will have to work out:

  • How much paint you need and how much it will cost.
  • How many packs of parquet you have to buy.
  • How many skirting-board lengths you need.
  • And finally, the total budget for the renovation.

Remember: if you choose eco-friendly paint, the price goes up by 20 %. Is it worth spending a bit more to look after the environment?

Prior knowledge
  1. Geometry and measurement: areas of plane figures (square, rectangle, triangle, circle); base area of solids; volumes: prism $V = A_{\text{base}} \cdot h$, cylinder $V = \pi r^2 h$, pyramid $V = \frac{1}{3} A_{\text{base}} \cdot h$.
  2. Units: length, area and volume units, and how they relate to litres: $1\ \text{dm}^3 = 1$ L and $1\ \text{m}^3 = 1000$ L.
  3. Arithmetic and proportion: rule of three, percentages and operations with decimals and with $\pi$.
  4. Equations: turning a statement into an equation, solving for the unknown (for example $a^2 = 12$) and square roots.
  5. Context: interpreting the results (litres, days, free space) and checking that they make sense.

The flat

Living room

4 m × 5 m × 2,5 m

Walls painted, parquet and skirting board

Bedroom 1

3 m × 4 m × 2,5 m

Walls painted

walls to paint   parquet floor   skirting board

Other rooms (not painted or renovated in this challenge):

width × length × height
Bedroom 22,5 m × 3 m × 2,5 m
Kitchen2 m × 3 m × 2,5 m
Bathroom2 m × 2 m × 2,5 m

Materials and prices

MaterialCoveragePrice
Wall paint1 tin covers 10 m²15 €
Eco-friendly paint1 tin covers 10 m²15 € + 20 %
Parquet1 pack covers 2 m²20 €
Wooden skirting board1 length is 2 m5 €

Part 1: Paint

Task 1

Work out the area of the living-room walls.

See the solution

There are two walls of $4 \times 2{,}5$ and two of $5 \times 2{,}5$:

$$2 \cdot (4 \cdot 2{,}5 + 5 \cdot 2{,}5) = 2 \cdot (10 + 12{,}5) = 45\ \text{m}^2$$

Doors and windows are not subtracted: the problem does not give their sizes.

Living-room walls: $45\ \text{m}^2$

Task 2

Work out the area of the walls of bedroom 1.

See the solution

There are two walls of $3 \times 2{,}5$ and two of $4 \times 2{,}5$:

$$2 \cdot (3 \cdot 2{,}5 + 4 \cdot 2{,}5) = 2 \cdot (7{,}5 + 10) = 35\ \text{m}^2$$

Bedroom 1 walls: $35\ \text{m}^2$

Task 3

Find the total area to paint and work out how many tins you need.

See the solution
$$45 + 35 = 80\ \text{m}^2$$
$$80 : 10 = 8 \text{ tins}$$

Here the division is exact. If it were not, you would round up: you cannot buy half a tin.

$80\ \text{m}^2$ to paint: $8$ tins are needed

Task 4

Work out the total cost of the paint.

See the solution
$$8 \cdot 15 = 120 \text{ €}$$

The paint costs $120$ €

Part 2: Parquet

Task 5

Work out the area of the living-room floor.

See the solution
$$4 \cdot 5 = 20\ \text{m}^2$$

Living-room floor: $20\ \text{m}^2$

Task 6

Work out how many packs of parquet are needed.

See the solution
$$20 : 2 = 10 \text{ packs}$$

$10$ packs of parquet are needed

Task 7

Work out the cost of the parquet.

See the solution
$$10 \cdot 20 = 200 \text{ €}$$

The parquet costs $200$ €

Part 3: Skirting board

Task 8

Work out the perimeter of the living room.

See the solution

The skirting board runs round the living-room floor, a $4 \times 5$ rectangle:

$$2 \cdot (4 + 5) = 18 \text{ m}$$

Perimeter: $18$ m

Task 9

Work out how many skirting-board lengths you need.

See the solution
$$18 : 2 = 9 \text{ lengths}$$

$9$ skirting-board lengths are needed

Task 10

Work out the total cost of the skirting board.

See the solution
$$9 \cdot 5 = 45 \text{ €}$$

The skirting board costs $45$ €

Part 4: Final budget

Task 11

Work out the total budget for the renovation (paint + parquet + skirting board).

See the solution
$$120 + 200 + 45 = 365 \text{ €}$$

Total budget: $365$ €

Task 12

If the paint were eco-friendly (+20 % on the price), what would the new budget be?

See the solution

A tin of eco-friendly paint costs $20\ \%$ more:

$$8 \cdot 15 \cdot 1{,}2 = 120 \cdot 1{,}2 = 144 \text{ €}$$

Only the paint changes; the parquet and the skirting board cost the same:

$$144 + 200 + 45 = 389 \text{ €}$$

Eco-friendly paint raises the budget by $389 - 365 = 24$ €, that is $\tfrac{24}{365} \cdot 100 \approx 6{,}58\ \%$ of the total.

With eco-friendly paint: $389$ €

Summary of results

See the solution
MaterialQuantityCostWith eco-friendly paint
Paint8 tins120 €144 €
Parquet10 packs200 €200 €
Skirting board9 lengths45 €45 €
Total365 €389 €