Ex.11.1 Q4 Mensuration Solutions - NCERT Maths Class 8

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Question

A flooring tile has the shape of a parallelogram whose base is \(24 \rm\,cm\) and the corresponding height is \(10 \rm\,cm.\) How many such tiles are required to cover a floor of area \({\rm{1080}}\,\,{{\rm{m}}^2}\)? (If required you can split the tiles in whatever way you want to fill up the corners).

Text Solution

What is Known?

Shape of the tile and its dimensions.

What is unknown?

Number of tiles that are required to cover a floor of area\(=\)\(1080\,\,{{\rm{m}}^2}\)

Reasoning:

Shape of the tile is parallelogram and its area can be found easily.

Area of parallelogram \(=\) Base \(\times\) Height

Steps:

Area of parallelogram

\[\begin{align} &= \text{base}\times \text{height} \\  &=24\,\text{cm}\times 10\,\text{cm}\\&=240\,\text{c}{{\text{m}}^{2}}\end{align}\]

Hence the area of one tile \( = 240\,{\rm{c}}{{\rm{m}}^2}\)

Area of the floor \( = 1080{{\rm{m}}^2}\,\,\left( {{\rm{given}}} \right)\)
\(\therefore \) Required number of tiles \(\begin{align} = \frac{{{\text{Area of the floor}}}}{{{\text{Area of one tile}}}}\end{align}\)

\[\begin{align}& =\frac{1080\,{{\text{m}}^{2}}}{240\,\,\text{c}{{\text{m}}^{2}}} \\ & =\frac{(1080\!\times \!10000){{\text{cm}}^{2}}}{240\text{c}{{\text{m}}^{2}}}\\&(\because 1\,\text{m }\!\!=\!100\,\text{cm}) \\ & =45000\,\,\,\text{tiles} \\\end{align}\]

Thus,\( 45000\) tiles are required to cover a floor of area \(1080 \rm{m^2}\)

  
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