Question

A flooring tile has the shape of a parallelogram whose base is 24 cm and its corresponding height is 10 cm. How many such tiles are required to fill a floor of area $1080\,{{m}^{2}}$?

Answer 1

Hint: The total area to be filled will be equal to the area of a single tile multiplied by the total number of tiles required. Each tile is of the shape of a parallelogram whose dimensions are given. Area of a parallelogram is the product of its height and base. Use appropriate conversion of units (1m=100cm).

Complete step-by-step answer:
We are given, total area of the floor $=1080\,{{m}^{2}}$
Since the area of the floor and dimensions of a single tile are given in different units, we need a conversion to make all the quantities to the same unit.
Therefore, total area of the floor $=1080\,{{m}^{2}}=1080\times 100\times 100\,c{{m}^{2}}$ (As 1m=100cm)
We are to find the number of tiles required to cover this area.
The dimensions of the tiles are given. A single tile is in the shape of a parallelogram with the length of its base as 24cm and its height as 10cm.

We know that,
Area of a parallelogram = Height $\times $ base
$\therefore $ Area of a single tile = $24\,cm\,\times \,10\,cm$
  = $240\,c{{m}^{2}}$
To find the number of tiles required to cover the floor we have to divide the total area of the floor by the area of a single tile.
$\therefore $ $Number\text{ }of\text{ }tiles\,\,=\,\,\,\,\dfrac{Total\,area}{Area\,of\,one\,tile}$
 =$\,\,\dfrac{1080\,\times 100\,\times 100\,c{{m}^{2}}}{240\,c{{m}^{2}}}$
=$\,\,45000$
Hence the number of tiles required to cover the floor is 45000.

Note: Key point used is that the total area to be filled will be equal to the area of single tile multiplied by the total number of tiles. Once we find the area of the parallelogram shaped tile using the established formula, we only need to do a basic division. One has to be careful to keep every quantity in the same unit while doing calculation. One also has to note that the number of tiles is a unit-less quantity.