Question

500 square tiles of side 25cm are laid across the hall of a room. What is the area of the hall is sq m​

Answer 1

$\sf\Large{\underline{\underline{Answer:-}}}$

${\underline{\underline{\sf{\green{Given,}}}}}$

• Total number of tiles laid = 500
• Side of tiles = 25cm
• Find the Area of hall in sq.m

⠀

First we need to find the area of each tile.

Formula using here

$\large{\sf {\blue{\boxed{\sf area \:of \:tiles = {(side)^{2}}}}}}$

Substitute the values,

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{{(25)^{2} }\:}}\end{gathered}$

$\: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{{625^{2} }\:}}\end{gathered}$

Thus, the area of each tile is 625cm².

⠀

Now, to find the area of hall we need to multiply the total number of tiles with the area of each tile.

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area \: of \: hall\;=\;\bf{{number \: of \: tiles \times area \: of \: all \: the \: tiles}{100}\:}}\end{gathered}$

$\: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;area \: of \: hall\;=\;\bf{{500 \times 625}\:}}\end{gathered}$

$\: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;area \: of \: hall\;=\;\bf{{312500cm^{2} }\:}}\end{gathered}$

We are asked to find the area of hall in sq.m,

we know 1cm² = $\frac{1}{10000}m^{2}$

So,

$\: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{{ \frac{1}{10000} \times 312500 }\:}}\end{gathered}$

$\: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{{ \frac{312500}{10000} }\:}}\end{gathered}$

$\longrightarrow$ Area = $\sf{\cancel\dfrac{312500}{10000}}$

$\: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{{ {31.25m ^{2} }} \:}}\end{gathered}$

${\underline{\underline{\sf{\green{Hence,}}}}}$

The area of hall is 31.25m².

Answer 2

$\sf\Large{\underline{\underline{Answer:-}}}$

${\underline{\underline{\sf{\green{Given,}}}}}$

Total number of tiles laid = 500

Side of tiles = 25cm

Find the Area of hall in sq.m

⠀

First we need to find the area of each tile.

Formula using here

$\large{\sf {\blue{\boxed{\sf area \:of \:tiles = {(side)^{2}}}}}}$

Substitute the values,

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{{(25)^{2} }\:}}\end{gathered}$

$\: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{{625^{2} }\:}}\end{gathered}$

Thus, the area of each tile is 625cm².

⠀

Now, to find the area of hall we need to multiply the total number of tiles with the area of each tile.

$\begin{gathered}\\\;\sf{:\rightarrow\;\;area \: of \: hall\;=\;\bf{{number \: of \: tiles \times area \: of \: all \: the \: tiles}{100}\:}}\end{gathered}$

$\: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;area \: of \: hall\;=\;\bf{{500 \times 625}\:}}\end{gathered}$

$\: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;area \: of \: hall\;=\;\bf{{312500cm^{2} }\:}}\end{gathered}$

We are asked to find the area of hall in sq.m,

we know 1cm² = $\frac{1}{10000}m^{2}$

So,

$\: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{{ \frac{1}{10000} \times 312500 }\:}}\end{gathered}$

$\: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{{ \frac{312500}{10000} }\:}}\end{gathered}$

$\longrightarrow$ Area = $\sf{\cancel\dfrac{312500}{10000}}$

$\: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;area\;=\;\bf{{ {31.25m ^{2} }} \:}}\end{gathered}$

${\underline{\underline{\sf{\green{Hence,}}}}}$

The area of hall is 31.25m².