Question

How many tiles each of area 400 ${cm}^2$, will be needed to pave a footpath which is 2m wide and surrounds a grass plot 25m long and 13m wide?

Answer 1

Hint: First find the area of the grass-plot. Now find the length and width of the footpath with the grassplot by adding the width of the footpath with the length and width of the grass plot. Then find the total area (grass plot + footpath). Now subtract the area of the grass-plot from the total area to find the area of the footpath around the plot. After that divide the footpath area by the area of the tiles to get the number of the tiles required for paving the footpath.

Formula used:
The area of the rectangular part is given by
$A = l \times b$
where l is length and b is the breadth

Complete step-by-step answer:
Given:-
The area of the tile is 400${cm}^2$ .
The length of the grass-plot is 25m.
The width of the grass plot is 13m.
Width of the footpath is 2m.
Let the number of tiles required for the paving be n, the area of the grass-plot be ${A_1}$, the total area of the plot (including footpath) be ${A_2}$ and the area of the footpath be ${A_3}$.
Now, the area of the grass plot is
${A_1} = 25 \times 13 = 325{m^2}$
The total length (grass plot + footpath) is,
$l = 2 + 25 + 2 = 29m$
The total width (grass plot + footpath) is,
$b = 2 + 13 + 2 = 17{m^{}}$
Then, the total area (grass plot + footpath) is,
${A_2} = 17 \times 29 = 493{m^2}$
So, the area of the footpath is calculated by subtracting the area of the grass-plot from the total area,
${A_3} = 493 - 325 = 168{m^2}$
Now, the number of tiles is calculated by the total area of the footpath by area of the tiles,
\[n = \dfrac{{168{m^2}}}{{400c{m^2}}}\]
Convert ${m^2}$into $c{m^2}$,
$n = \dfrac{{168 \times 10000c{m^2}}}{{400c{m^2}}}$
Cancel out the common factor from the numerator and denominator and multiply the remaining parts to get the answer,
$n = 4200$

Hence, the number of tiles required to pave the footpath is 4200.

Note: The students are likely to make mistakes in questions which have units in a different form. Students are advised to use common conversions first to convert all the values in the same unit and then do calculations.
When we have to calculate the total area (grass plot + footpath), the width of the footpath has to add twice in both length and width.