Tiling a floor: how many tiles, waste and cost

The plane and space, grade 10 (3 units) Lesson 12 of 15Learning

Tiling a floor: how many tiles, waste and cost

How many tiles

Tiling is covering a floor with tiles, with no gaps and no tile on top of another.

Example. A room of 4 m by 3 m, and square tiles of 50 cm by 50 cm.

Along the room: $\displaystyle {400\div50}={8}$ tiles.
Across the room: $\displaystyle {300\div50}={6}$ tiles.
In all: $\displaystyle {8\cdot6}={48}$ tiles.
A check by the areas: the room is $\displaystyle {4\cdot3}={12}$ m², a tile $\displaystyle {0.5\cdot0.5}={0.25}$ m², and $\displaystyle {12\div0.25}={48}$ .

Cut tiles

When the tiles do not fit a whole number of times, a cut tile goes at the end of the row – and it has to be bought too.

Example. A room of 3.3 m by 2.7 m, and tiles of 60 cm by 60 cm.

Along: $\displaystyle {330\div60}={5.5}$ – five whole tiles and half a tile, that is 6 tiles.
Across: $\displaystyle {270\div60}={4.5}$ , that is 5 tiles.
In all: $\displaystyle {6\cdot5}={30}$ tiles.

Exercise 1

How many tiles are needed?

A room of 5 m by 4 m, tiles of 50 cm by 50 cm

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

A balcony of 4 m by 3.2 m, tiles of 40 cm by 40 cm

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

A room of 3.5 m by 2.2 m, tiles of 60 cm by 60 cm. How many tiles along, how many across, and how many in all?

Waste

During the work tiles break, and cutting leaves pieces that cannot be used. What is lost is called waste. So you buy more than the area – usually 10% more.

Example. A floor of 20 m², with 10% waste.
The tiles are sold in boxes, 1.44 m² in each box. A box costs 95 ₪.

The area to buy: $\displaystyle {20\cdot1.1}={22}$ m².
Boxes: $\displaystyle {22\div1.44}={15.3}$ – 15 boxes are not enough, so you buy 16.
The price: $\displaystyle {16\cdot95}={1{,}520}$ ₪.

Exercise 2

A floor of 35 m² is to be tiled, with 10% waste.
Each box of tiles holds 1.5 m².

The area to buy, in m²

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

How many boxes must be bought? Explain.

Exercise 3

A skirting board – a low strip at the bottom of the wall – is fixed along the walls of a room.
The room is 4 m by 3 m, and it has a doorway 0.8 m wide with no skirting.
A metre of skirting costs 25 ₪.

The length of the skirting, in metres

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

The price, in shekels

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

Exercise 4

A floor of 25 m². When buying the tiles, 10% waste is added; the laying is paid by the area of the floor only.
Tile A: 120 ₪ per m², and laying it costs 40 ₪ per m².
Tile B: 95 ₪ per m², but it is small, and laying it costs 60 ₪ per m².

The total cost with tile A, in shekels

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

The total cost with tile B, in shekels

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

Which tile is cheaper in the end, and by how many shekels?

/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

Formulas: the plane and space, grade 10 (3 units)

Open as a page

Perimeters

The perimeter of a rectangle – $\displaystyle a$ , $\displaystyle b$ two sides that meet at a vertex
$\displaystyle P$ $\displaystyle =$ $\displaystyle 2(a+b)$
The perimeter of a square – $\displaystyle a$ the side
$\displaystyle P$ $\displaystyle =$ $\displaystyle 4a$
Pi
$\displaystyle \pi\approx3.14$
The circumference – $\displaystyle d$ the diameter
$\displaystyle C$ $\displaystyle =$ $\displaystyle \pi d$
The circumference – $\displaystyle r$ the radius
$\displaystyle C$ $\displaystyle =$ $\displaystyle 2\pi r$

Routes: Pythagoras, distance, speed and time

Pythagoras’ theorem – $\displaystyle a$ , $\displaystyle b$ the legs, $\displaystyle c$ the hypotenuse
$\displaystyle c^2$ $\displaystyle =$ $\displaystyle a^2+b^2$
The hypotenuse
$\displaystyle c$ $\displaystyle =$ $\displaystyle \sqrt{a^2+b^2}$
A leg
$\displaystyle a$ $\displaystyle =$ $\displaystyle \sqrt{c^2-b^2}$
Speed – $\displaystyle s$ the distance, $\displaystyle t$ the time
$\displaystyle v$ $\displaystyle =$ $\displaystyle \frac{s}{t}$
Distance
$\displaystyle s$ $\displaystyle =$ $\displaystyle v\cdot t$
Time
$\displaystyle t$ $\displaystyle =$ $\displaystyle \frac{s}{v}$

Areas

The area of a rectangle
$\displaystyle A$ $\displaystyle =$ $\displaystyle a\cdot b$
The area of a square
$\displaystyle A$ $\displaystyle =$ $\displaystyle a^2$
The area of a triangle – $\displaystyle h_a$ the height to the side $\displaystyle a$
$\displaystyle A$ $\displaystyle =$ $\displaystyle \frac{a\cdot h_a}{2}$
The area of a parallelogram – $\displaystyle h_a$ the height to the side $\displaystyle a$
$\displaystyle A$ $\displaystyle =$ $\displaystyle a\cdot h_a$
The area of a trapezoid – $\displaystyle a$ , $\displaystyle b$ the bases, $\displaystyle h$ the height
$\displaystyle A$ $\displaystyle =$ $\displaystyle \frac{(a+b)\cdot h}{2}$
The area of a disc – $\displaystyle r$ the radius
$\displaystyle A$ $\displaystyle =$ $\displaystyle \pi r^2$
A square metre in square centimetres (a dunam is 1000 m²)
$\displaystyle 1\text{ m}^2=100\cdot100\text{ cm}^2=10000\text{ cm}^2$

Tilings

The sum of the angles of a polygon with $\displaystyle n$ sides
$\displaystyle 180^{\circ}\cdot(n-2)$
The angle of a regular polygon with $\displaystyle n$ sides
$\displaystyle \alpha$ $\displaystyle =$ $\displaystyle \frac{180^{\circ}\cdot(n-2)}{n}$
The angles around a vertex of a tiling
$\displaystyle \alpha_1+\alpha_2+\ldots=360^{\circ}$