In a parallelogram the lengths of the opposite sides are equal. Consider the parallelogram ABCD ( figure 4.3).
seg. AL and seg. BM are perpendiculars on the line containing CD. l (AL) is altitude of the parallelogram.
l (AB) = a
l (AD) = b
l (AL) = h
l (BM) = h
Consider D ALD and D BMC. Both are right triangles.
l (AD) = l (BC) opposite sides of a parallelogram.
l (AL) = l (BM) altitudes of a parallelogram.
\ D ALD @ D BMC
Therefore areas of these two triangles are equal.
Consider parallelograms ABCD and ABML. Their areas are equal.
Parallelogram ABML is a rectangle. Therefore area of ABML = a ´ h.
Thus area of a parallelogram is a product of one base and its corresponding altitude.
A = ah
The perimeter of the parallelogram = 2 ( a + b ).