Vaishali Bhatia and Rupesh Pathak Solutions for Chapter: Perimeter and Area, Exercise 5: Exercise 13.2

A rectangular lawn is to be surrounded externally by a path which is $3 \mathrm{m}$ wide. The dimensions of the lawn are $35 \mathrm{m}$ and $45 \mathrm{m}$. If the cost of constructing the path at the rate of $₹100$ per ${\mathrm{m}}^2$ is $₹k$, find $k$.

Two crossroads each $2 \mathrm{m}$ wide intersect each other at right angles through the centre of a rectangular area of dimension $75 \mathrm{m}\times 50 \mathrm{m}$. These crossroads run parallel to the sides of the rectangle. If the area of crossroads is $k {\mathrm{m}}^2$, find $k$.

A sheet of paper measures $40 \mathrm{cm}\times 20 \mathrm{cm}$. If a strip $4 \mathrm{cm}$ wide is cut from it all around, find the area of strip-cut out and the area of the remaining sheet of paper.

If the area of the shaded portion in the following rectangle $ABCD$ is $k$ sq. units, find $k$.

A verandah of width $2.1 \mathrm{m}$ is constructed all along outside a circular conference hall of radius $10.5 \mathrm{m}$. If the cost of cementing the floor of the verandah at the rate of $₹15.20$ per $\mathrm{sq}. \mathrm{m}.$ is $₹k$, find $k$ in decimal number. [Take $\mathrm{\pi }=\frac{22}{7}$]

A photo frame of dimensions $48 \mathrm{cm}$ by $32 \mathrm{cm}$ has a border of width $5 \mathrm{cm}$ around and inside it. Find the cost of decorating the border at the rate of $₹5.25$ per $\mathrm{sq}. \mathrm{cm}.$ and also find the area of the photo that can fit in the frame.

A saree of length $6 \mathrm{m}$ and breadth $1.8 \mathrm{m}$ has a border of width $15 \mathrm{cm}$ along its length on both sides and a border of width $50 \mathrm{cm}$ on one end of the breadth. If the area covered by the border in the saree is $k {\mathrm{cm}}^2$, find $k$.

A circular garden of radius $80 \mathrm{m}$ has a pathway around and outside it of width $3 \mathrm{m}$. If the cost of levelling the path at $₹7.50$ per ${\mathrm{m}}^2$ is $₹k$, find $k$ in decimal number. [Take $\mathrm{\pi }=3.14$]