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4.4 Parallelogram

In a parallelogram the lengths of the opposite sides are equal. Consider the parallelogram ABCD ( figure 4.3).

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 ).

[next page]

Index

4.1 Perimeter
4.2 Square
4.3 Rectangle
4.4 Parallelogram
4.5 Triangle
4.6 Trapezoids
4.7 Circles

Chapter 5

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