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# Arjun bought a rectangular plot with length $x$and breadth $y$. He then sold a triangular plot from it, whose base $y$ was and height $z$. Find the area of the remaining part of the plot

Last updated date: 04th Mar 2024
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Answer
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Hint: The area can be defined as the space occupied by a flat surface of an object. The area is the number of unit squares closed by figure. Perimeter is the total length of the sides of the two dimensional shape. Perimeter is always less than the area of the given figure. Because the perimeter is outer and the area is inner property.

Complete step-by-step solution:
Given,

Length of the plot, $l = x$
Breadth of the plot, $b = y$
Base of the plot, $b = y$
Height of the plot, $h = z$
The area of the rectangular plot,
As we know that
$\therefore {A_{rec\tan gle}} = l \times b$
Put the value
$\Rightarrow {A_{rec\tan gle}} = xy$
Now,
The area of triangular plot,
As we know that
$\therefore {A_{triangle}} = \dfrac{1}{2} \times length \times height$
Put the values
$\therefore {A_{triangle}} = \dfrac{{yz}}{2}$
Now the area of remaining part
$\therefore {A_{remain}} = {A_{rec\tan gle}} - {A_{triangle}}$
Put the value
$\Rightarrow {A_{remain}} = xy - \dfrac{{yz}}{2}$
Simplify
$\Rightarrow {A_{remain}} = \dfrac{y}{2}(2x - z)$

Note: For solving this type of problem we should have theoretical knowledge about the geometrical shapes like rectangle, square, triangle. We should have known the formulae and geometrical difference b/w area and perimeter of different shapes. Perimeter is the sum of all sides. Where the area is space occupied by the closed figure. Volume is how much an object will hold. There is not any direct relation between area and perimeter. But both of them totally depend on dimensions of the figure.