Question

Draw the graph of the equations x = 3 , x = 5 and 2x − y − 4 = 0 . Also, find the area of the quadrilateral formed by the lines and the x-axis.

Answer 1

The given equations are
x = 3 .....(i)
x = 5 .....(ii)
2x − y − 4 = 0 .....(iii)
For (iii), we have

x	0	2
y	−4	0

We plot the lines on the graph as follows:

The vertices of the quadrilateral thus formed are A(5, 0), B(5, 6), C(3, 2) and D(3, 0).
∴ Area of the quadrilateral DABC
= Area of a trapezium
= $\frac{1}{2}h\left(a+b\right)$
$$\begin{gathered} =\frac{1}{2}\times 2\times \left(2+6\right) \\ =8\mathrm{square}\mathrm{units} \end{gathered}$$
Thus, the area of the quadrilateral formed by the given lines and the x-axis is 8 square units.