Question & Answer

A flooring tile has a shape of parallelogram whose base is 18 cm and the corresponding height is 6 cm. How many such tiles are required to cover a floor of area $540{{m}^{2}}$. (If required you can split the tiles in whatever way you want to fill up the corners)

ANSWER Verified Verified
Hint: In this problem we are given the base and height of a parallelogram. Using this data, we can calculate the individual tile area which is in shape of a parallelogram. Dividing it with the given area in the problem statement will give the number of tiles involved.

Complete step-by-step answer:
In Geometry, a parallelogram is a two-dimensional figure with four sides. A parallelogram has two pairs of parallel sides with equal measures. Since it is a two-dimensional figure, it has an area and perimeter.
In this question, first we find the area of parallelogram using the formula $b\times h$ where b is the base and h is the height of the parallelogram.
As, we know that $1m=100cm$. Using this, first we convert the base of parallelogram and height of parallelogram from centimeters to meters.
Base of parallelogram$=18cm=0.18m$.
Height of parallelogram$=6cm=0.06m$.
Area of parallelogram$=b\times h=0.18\times 0.06$.
Area of parallelogram$=0.0108{{m}^{2}}$.
Now, the number of tiles required can be expressed as $\dfrac{Area\text{ }of\text{ floor}}{Area\text{ of each tile}}$.
As given in the problem statement, the area of the floor is 540 square meter and the area of each tile obtained is 0.0108 square meter. By putting these values in the above expression, we get
Number of tiles required$=\dfrac{540{{m}^{2}}}{0.0108{{m}^{2}}}=50000$ tiles.
Hence, the number of tiles required to cover a floor of $540{{m}^{2}}$ is 50000.

Note: The key step for solving this problem is the knowledge of the area of parallelogram. This is a direct question but students must take care of units while calculating the area. Both the units in the division term must be the same to obtain the correct answer.