Question

a floor of length 7m and breadth 4m is to be covered by square tiles each of side 20 cm . how many tiles are needed to cover the floor? area of the floor ______ sq cm. area of one tile _______ sq cm. number of tiles=__________

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

Length of floor = 7 m = 700 cm

Breadth of floor = 4 m = 400 cm

So,

$\rm \: Area_{(floor)} = Length \times Breadth$

$\rm \: Area_{(floor)} = 700 \times 400$

$\rm\implies \:\boxed{ \rm{ \:Area_{(floor)} = 280000 \: {cm}^{2} \: }}$

Now, Side of square tile = 20 cm

$\rm \: Area_{(tile)} \: = \: {(side)}^{2}$

$\rm \: Area_{(tile)} \: = \: {20}^{2}$

$\rm\implies \:\boxed{ \rm{ \:Area_{(tile)} \: = \: 400 \: {cm}^{2} \: \: }}$

Let assume that n square tiles of side 20 cm be required to cover the floor.

Thus,

$\rm \: n \times Area_{(tile)} = Area_{(floor)}$

$\rm \: n \times 400 = 280000$

$\rm\implies \:\boxed{ \rm{ \: n\: = \: 700 \: \: }}$

So,

$\rm\implies \:\boxed{ \rm{ \: Number \: of \: tiles\: = \: 700 \: \: }}$

$\rule{190pt}{2pt}$

Additional information :-

$\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Base\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Base\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}$

Answer 2

Step-by-step explanation:

\large\underline{\sf{Solution-}}

Solution−

Given that,

Length of floor = 7 m = 700 cm

Breadth of floor = 4 m = 400 cm

So,

\begin{gathered}\rm \: Area_{(floor)} = Length \times Breadth \\ \end{gathered}

Area

(floor)

=Length×Breadth

\begin{gathered}\rm \: Area_{(floor)} = 700 \times 400 \\ \end{gathered}

Area

(floor)

=700×400

\begin{gathered}\rm\implies \:\boxed{ \rm{ \:Area_{(floor)} = 280000 \: {cm}^{2} \: }} \\ \end{gathered}

⟹

Area

(floor)

=280000cm

2

Now, Side of square tile = 20 cm

\begin{gathered}\rm \: Area_{(tile)} \: = \: {(side)}^{2} \\ \end{gathered}

Area

(tile)

=(side)

2

\begin{gathered}\rm \: Area_{(tile)} \: = \: {20}^{2} \\ \end{gathered}

Area

(tile)

=20

2

\begin{gathered}\rm\implies \:\boxed{ \rm{ \:Area_{(tile)} \: = \: 400 \: {cm}^{2} \: \: }} \\ \end{gathered}

⟹

Area

(tile)

=400cm

2

Let assume that n square tiles of side 20 cm be required to cover the floor.

Thus,

\begin{gathered}\rm \: n \times Area_{(tile)} = Area_{(floor)} \\ \end{gathered}

n×Area

(tile)

=Area

(floor)

\begin{gathered}\rm \: n \times 400 = 280000 \\ \end{gathered}

n×400=280000

\begin{gathered}\rm\implies \:\boxed{ \rm{ \: n\: = \: 700 \: \: }} \\ \end{gathered}

⟹

n=700

So,

\begin{gathered}\rm\implies \:\boxed{ \rm{ \: Number \: of \: tiles\: = \: 700 \: \: }} \\ \end{gathered}

⟹

Numberoftiles=700

\rule{190pt}{2pt}

Additional information :-

\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Base\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Base\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}\end{gathered}

†

FormulasofAreas:−

⋆Square=(side)

2

⋆Rectangle=Length×Breadth

⋆Triangle=

2

1

×Base×Height

⋆Scalene△=

s(s−a)(s−b)(s−c)

⋆Rhombus=

2

1

×d

1

×d

2

⋆Rhombus=

2

1

d

4a

2

−d

2

⋆Parallelogram=Base×Height

⋆Trapezium=

2

1

(a+b)×Height

⋆EquilateralTriangle=

4

3

(side)

2