Question

Determine area(in sq. units) of trapezium, the equations of whose sides are $x=0,y=0,y=4$ and $2x+y=6$.

• A. $7$
• B. $8$
• C. $9$
• D. $10$

Answer 1

The correct option is B $8$

Clearly $x=0$ represents Y-axis and $y=0$ represents X axis.

$y=4$ for every value of $x$.

So let A(3,4), B(0,4) be two points on the line represented by y=4. In the graph the points are plotted.

For $2x+3y=6$

Put $y=0;$ we get $x=3$ and $x=0$ we get $y=6$

From the graph we can see that the lines represented form a trapezium $OCEB$

The coordinates of its vertices are

$O(0,0),C(3,0),E(1,4),B(0,4)$

Area of trapezium=$\frac{1}{2}\times (OC+BE)\times OB=\frac{1}{2}(3+1)\left(4\right)=8sq.units$