R. D. Sharma Solutions for Chapter: Mensuration – I (Perimeter and Area of Rectilinear Figures), Exercise 2: EXERCISE

A square lawn has a $2 \mathrm{m}$ wide path surrounding it. If the area of the path is $136 {\mathrm{m}}^2$, find the area of the lawn.

A poster of size $10 \mathrm{cm}$ by $8 \mathrm{cm}$ is pasted on a sheet of cardboard such that there is a margin of width $1.75 \mathrm{cm}$ along each side of the poster. Find the total area of the margin and the cost of the cardboard used at the rate of $₹0.60 per {\mathrm{cm}}^2$.

A rectangular field is $50 \mathrm{m}$by $40 \mathrm{m}$. It has two roads through its centre, running parallel to its sides. The widths of the longer and shorter roads are $1.8 \mathrm{m}$ and $2.5 \mathrm{m}$ respectively. Find the area of the roads and the area of the remaining portion of the field.

There is a rectangular field of size $94 \mathrm{m}\times 32 \mathrm{m}$. Three roads each of $2 \mathrm{m}$ width pass through the field such that two roads are parallel to the breadth of the field and the third is parallel to the length. Calculate the area of the field covered by the three roads and area of the field not covered by the roads.

A school has a hall which is $22 \mathrm{m}$ long and $15.5 \mathrm{m}$ broad. A carpet is laid inside the hall leaving all around a margin of $75 \mathrm{cm}$ from the walls. Find the area of the carpet and the area of the strip left uncovered. If the width of the carpet is $82 \mathrm{cm}$, find the cost at the rate of $₹18$ per metre.

Two cross roads, each of width $5 \mathrm{m}$, run at right angles through the centre of a rectangular park of length $70 \mathrm{m}$ and breadth $45 \mathrm{m}$ parallel to its sides. Find the area of the roads. Also, find the cost of constructing the roads at the rate of $₹105 per {\mathrm{m}}^2$.

The length and breadth of a rectangular park are in the ratio $5: 2$. A  $2.5 \mathrm{m}$ wide path running all around the outside the park has an area $305 {\mathrm{m}}^2$. Find the dimensions of the park.

A square lawn is surrounded by a path $2.5 \mathrm{m}$ wide. If the area of the path is $165 {\mathrm{m}}^2$, find the area of the lawn.