Problem Solving

In the rectangular coordinate system above, the area of parallelogram KLMN is :-

a) 6/sqrt3
b) 6
c) 6sqrt3
d) 12
e) cannot be determined.

Answer is B.

The opposite sides of a parallelogram are parallel to each other. So since side NM lies on the x axis, side KL must be parallel to the x axis.

Therefore all points on side KL are the same distance from the x axis, meaning that if L is 3 above the x axis, b = 3, and K is also 3 above the x axis.

area of a parallelogram = base x height

Since all points on KL are 3 above the x axis, on which NM lies, the height of the parallelogram is 3.

Meanwhile, since the y coordinates for K and L are the same, the length of KL is simply the change in x. So KL is 2 long.

So using KL as the base, we get area = 2 x 3 = 6.

The correct answer is B.