Calculate Parallelogram Area: Using 6-Unit Height and 9-Unit Base with Perpendicular Lines

ABCD is a parallelogram.

Angle ACB is equal to angle EBC.

BF = 6

CE = 9

BF is perpendicular to DE.

Calculate the area of the parallelogram.

Given that angle ACB is equal to angle CBE, it follows that AC is parallel to BE

since alternate angles between parallel lines are equal.

As we know that ABCD is a parallelogram, AB is parallel to DC and therefore AB is also parallel to CE since it is a line that continues DC.

Given that AC is parallel to BE and, in addition, AB is parallel to CE, it can be argued that ABCE is a parallelogram and, therefore, each pair of opposite sides in a parallelogram are parallel and equal.

From this it is concluded that AB=CE=9

Now we calculate the area of the parallelogram ABCD according to the data.

$S_{ABCD}=AB\times BF$

We replace the data accordingly:

$S_{ABCD}=9\times6=54$