Question

Arjun bought a rectangular plot with length x and breadth y and then sold a triangular part of it whose base is y and height is z. Find the area of the remaining part of the plot.

Answer 1

Given, Arjun bought a rectangular plot with length x and breadth y

∴ Area of rectangular plot = Length × Breadth = x × y = xy

Also, given triangular part with base y and height z is sold

So, area of triangular part = ${\displaystyle \frac{1}{2}\times y\times z=\frac{1}{2}yz}$ ......${\displaystyle [\because \text{Area of triangle}=\frac{1}{2}\times \text{height}\times \text{base}]}$

∴ Area of remaining part of the plot = Area of rectangular plot – Area of triangular plot = ${\displaystyle xy-\frac{1}{2}yz}$ = ${\displaystyle y(x-\frac{1}{2}z)}$.