R. D. Sharma Solutions for Chapter: Mensuration-I (Area of a Trapezium and a Polygon), Exercise 1: EXERCISE

Find the area of a rhombus whose side is $6\mathrm{cm}$ and whose altitude is $4\mathrm{cm}$. If one of its diagonals is $8\mathrm{cm}$ long, find the length of the other diagonal.

A rectangular grassy plot is $112 \mathrm{m}$ long and $78 \mathrm{m}$ broad. It has a gravel path $2.5 \mathrm{m}$ wide all around it on the side. Find the area of the path and the cost of constructing it at $₹4.50$ per square metre.

The length of a side of a square field is $4 \mathrm{m}$. What will be the altitude of the rhombus, if the area of the rhombus is equal to the square field and one of its Diagonal is $2 \mathrm{m}$$?$

In exchange for a square plot one of whose sides is $84 \mathrm{m}$, a man wants to buy a rectangular plot $144 \mathrm{m}$ long and of the same area as of the square plot. Find the width (in $\mathrm{m}$) of the rectangular plot.

The area of a rhombus is $84 {\mathrm{m}}^2$. If its perimeter is $40 \mathrm{m}$, then find its altitude (in $\mathrm{m}$).

A garden is in the form of a rhombus whose side is $30 \mathrm{m}$ and the corresponding altitude is $16 \mathrm{m}$. Find the cost of leveling the garden at the rate of $\mathrm{₹}2 \mathrm{per} {\mathrm{m}}^2$.

A field in the form of a rhombus has each side of length $64 \mathrm{m}$ and altitude $16 \mathrm{m}$. What is the side of a square (in $\mathrm{m}$) field which has the same area as that of a rhombus?

The area of a rhombus is equal to the area of a triangle whose base and the corresponding altitude are $24.8 \mathrm{cm}$ and $16.5 \mathrm{cm}$ respectively. If one of the diagonals of the rhombus is $22 \mathrm{cm}$, find the length of the other diagonal (in $\mathrm{cm}$).