Applications of Area and Perimeter in Real Life

A path of $1 \mathrm{m}$ wide runs around and inside a rectangular garden of length $40 \mathrm{m}$ and width $20 \mathrm{m}$. Find the cost of levelling the path at the rate of $\mathrm{Rs}. 3.75 \mathrm{per} \mathrm{square} \mathrm{metre}$.  (in $\mathrm{Rs}.$)

The length and breadth of a rectangular filed are $10 \mathrm{m}$ and $8 \mathrm{m}$, respectively. Two rectangular paths each $3 \mathrm{m}$ wide run inside the plot, one along the length and the other along the breadth. Find the total area occupied by the paths.

A path of $3 \mathrm{m}$ wide runs around and outside a rectangular playground of length $15 \mathrm{m}$ and width $10 \mathrm{m}$. Find the area of the path. (in ${\mathrm{m}}^2$)

The length and breadth of a rectangular field are $4 \mathrm{m}$ and $3 \mathrm{m}$ respectively. The field is divided into two parts by fencing it diagonally. Find the cost of fencing at $\mathrm{Rs}. 10$ per metre.

The hospital is on a rectangular land with a boundary wall all around. Leaving the boundary wall, the length of the land is $70 \mathrm{m}$ and its breadth is $60 \mathrm{m}$. If  two paths pass through the middle of the rectangular plot of land of hospital (the figure is shown in the image below), the total area of two paths is

In the figure given below, find the area (in $\mathrm{sq}.\mathrm{cm}.$) of the coloured portion:

In the figure given below, the area of the shaded portion is

David drawn the picture given below. Find the area of the black coloured roads(in $\mathrm{sq}.\mathrm{cm}$).

A picture is painted on a cardboard $8 \mathrm{c}\mathrm{m}$ long and $5 \mathrm{c}\mathrm{m}$ wide such that there is a margin of $1.5 \mathrm{c}\mathrm{m}$ along each of its sides. Find $\mathrm{k}$, if the total area of the margin is $\mathrm{k} {\mathrm{cm}}^2$.

A slate is $35 \mathrm{cm}$ long and $20 \mathrm{cm}$ wide. It is surrounded by a wooden frame of width $2.5 \mathrm{cm}$ all around. The area of the wooden frame is $K {\mathrm{cm}}^2$, find the value of $K.$

A rectangular garden $10 \mathrm{m}$ by $16 \mathrm{m}$ is to be surrounded by a concrete walk of uniform width. Given that the area of walk is $120$ sq m. assuming the width of the walk to be $x$, form an equation in $x$ and solve it to find the value of $x$.

A path $1 \mathrm{m}$ wide is built along the border and inside a square garden of side $30 \mathrm{m}.$ If area of the path is $k {\mathrm{m}}^2$then, find the value of $k$.

A paddy field is in a square shape and has side length equal to $45$ $\mathrm{m}$. Babu Ram hires a labour to harves t the paddy from the field. The labour says that he will charge $₹$$15$ per $\mathrm{sq}.\mathrm{m}.$ Being uneducated he demands $₹$$25,000$ for the whole work. Babu Ram calculates the actual amount to be paid to the labour and gives that amount to labour. What is the actual amount to be paid? What value of Babu Ram is depicted here?

A lane $150 \mathrm{m}$ long and $5 \mathrm{m}$ wide is to be paved with tiles of length $20 \mathrm{c}\mathrm{m}$ and breadth $15 \mathrm{cm}$. If the cost of the tiles is $₹750$ per $1000$ tiles, find the total cost of the tiles required.

A square lawn with side $30 \mathrm{m}$ is surrounded externally by a path which is$2 \mathrm{m}$ wide. Find the area of the path and calculate the cost of levelling the path at $₹ 2.50$per ${\mathrm{m}}^2$.

A rectangular floor of length $9 \mathrm{m}$ and breadth $6 \mathrm{m}$ has black tiles laid in the given pattern. Find the number of tiles laid, if each tile has dimensions $40 \mathrm{cm}\times 10 \mathrm{cm}$.

A playground is $750 \mathrm{m}$ long and $250 \mathrm{m}$ broad. Find the cost of levelling at $₹16$ per $100 \mathrm{sq}.\mathrm{m}$.

A room is $10.2 \mathrm{m}$ long, $8.5 \mathrm{m}$ wide and $4.6 \mathrm{m}$ high. It has a door measuring $1.5 \mathrm{m}\times 2.6 \mathrm{m}$ and a window measuring $2 \mathrm{m}\times 1.7 \mathrm{m}$. Find the cost of tiling the walls at the rate of $₹13.50$ per sq.m

A room is $20\mathrm{m}$ long and $15\mathrm{m}$ broad. It has to be carpeted after leaving a margin of $2\mathrm{m}$ all around it. Find the area of the carpet required and the cost of carpeting it at $₹800$ per ${\mathrm{m}}^2.$

A room is $6$ $\mathrm{m}$ long and $5$ $\mathrm{m}$ wide. It has a $50$ $\mathrm{cm}$ wide verandah all around it. Calculate the area of the verandah.