The diagonals of a field in the form of a quadrilateral are $106\ m$ and $80\ m$ and intersect each other at right angles. Find the cost of cultivating the field at the rate of Rs. $25.50$ per $100\ m^2$.

Given: The diagonals of a field in the form of a quadrilateral are $106\ m$ and $80\ m$ and intersect each other at right angles. Rate of Rs. $25.50$ per $100\ m^2$.

To do: To find the cost of cultivating the field.

Solution:

In the quadrilateral, the diagonals bisects at right angles.

$\therefore$ The quadrilateral is a rhombus.

Area of the rhombus$=\frac{1}{2}\times d_1\times d_2$

$=\frac{1}{2}\times106\times80$

​

$=4240\ m^2$

Cost of cultivating the field at Rs. $25.50$ per $100\ m^2$

$=\frac{1}{2}\times 4240\times 25.5$

​

$= Rs.\ 1081.20$

Thus, total cost of cultivating the field is $Rs.\ 1081.20$.

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Updated on: 10-Oct-2022

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