In the figure below, is a parallelogram in which
and , where cm
and cm. Find the area of .
Step 1: Establish that .
The converse of pythagoras' theorem states that if the square of the length of a side is equal to the sum of the squares of the other two sides,
then the angle opposite to this side is a right angle. For ,
Since , then and .
Since is a right angle, then and can be used as the height of the parallelogram.
Step 2: Find the parallelogram's area.
Since opposite sides of a parallelogram are equal in length, then cm.
Use the formula for the area of a parallelogram, with as the base and as the height.