R K Bansal Solutions for Chapter: Area of a Trapezium and a Polygon, Exercise 2: EXERCISE 20(B)

In the following case ABCD is a square and PQRS is a rectangle. If the area of the shaded portion is $k {\mathrm{m}}^2$, find $k$.

(All measurements are in meter)

A path of uniform width, $3 \mathrm{m}$, runs around the outside of a square field of side $21 \mathrm{m}$. If the area of the path is $k {\mathrm{cm}}^2$, find $k$.

A path of uniform width $2.5 \mathrm{m}$, runs around the inside of a rectangular field $30 \mathrm{m} \mathrm{by} 27 \mathrm{m}$. If the area of the path is $k {\mathrm{cm}}^2$, find $k$.

A rectangular field is $30 \mathrm{m}$ in length and $22 \mathrm{m}$ in width. Two mutually perpendicular roads, each $2.5 \mathrm{m}$ wide are drawn inside the field so that one road is parallel to the length of the field and the other road is parallel to its width.

If the area of the cross roads is $k {\mathrm{m}}^2$, find $k$.

The length and the breadth of rectangular field are in the ratio $5:4$ and its area is $3380 {\mathrm{m}}^2$. If the cost of fencing it at the rate of $₹75$ per metre is $₹k$, find $k$.

The length and breadth of a conference hall are in the ratio $7:4$ and its perimeter is $110 \mathrm{m}$. If area of the floor of the hall is $k {\mathrm{m}}^2$, find $k$.

The length and breadth of a conference hall are in the ratio $7:4$  and its perimeter is $110 \mathrm{m}$. Find the number of tiles each a rectangle of size $2.5 \mathrm{cm}\times 20 \mathrm{cm}$, required for flooring of the hall.

The length and breadth of a conference hall are in the ratio $7:4$ and its perimeter is $110 \mathrm{m}$. Find the cost of the tiles at the rate of  $₹1400$ per hundred tiles.