R. S. Aggarwal Solutions for Chapter: Area, Exercise 2: EXERCISE 23B

The base of a triangular field is three times its height. If the cost of cultivating the field at $\mathrm{Rs}.60$ per hectare is $\mathrm{Rs}.810$. Find the base and height of the field.

The perimeter of a rectangular field is $0.6 \mathrm{km}$ and its length is twice its breadth. Determine the area of the field in hectares.

The area of a parallelogram is $338{ \mathrm{m}}^2$. If its altitude is twice the corresponding base, determine the base and altitude.

The two parallel sides of a trapezoidal field measure $58 \mathrm{m}$ and $42 \mathrm{m}$ respectively. The other two sides are equal, each being $17 \mathrm{m}$. Find its area.

The cost of ploughing a trapezoidal field at $\mathrm{Rs}.25$ per sq.metre is $\mathrm{Rs}.7800$. The difference between its parallel sides is $8$ metres and the perpendicular distance between them is $24 \mathrm{m}$. Find the lengths of parallel sides.

Find the area of a quadrilateral piece of ground one of whose diagonals is $50 \mathrm{m}$ long and the lengths of perpendiculars from the other two vertices are $29 \mathrm{m}$ and $21 \mathrm{m}$ respectively.

Find the area of a parallelogram whose two adjacent sides are $130 \mathrm{m}$ and $140 \mathrm{m}$ and the length of the diagonal connecting the end points of these sides is $150 \mathrm{m}$. Find the cost of gravelling it at $15$paise per m².

Find the area of a quadrilateral piece of ground $\mathrm{ABCD}$ in which $\mathrm{AB}=143 \mathrm{m}$, $\mathrm{BC}=154 \mathrm{m},\mathrm{AC}=165 \mathrm{m},\mathrm{CD}=60 \mathrm{m}$ and $\mathrm{AD}=125 \mathrm{m}$.