Lauretta J. Fox
A parallelogram is a four-sided polygon whose opposite sides are parallel. Any side of the parallelogram may be called a base. Unlike the rectangle, the consecutive sides of a parallelogram are not always perpendicular, thus the altitude of the parallelogram is not necessarily a side of the figure. The altitude is any segment drawn from a point on one side of the parallelogram perpendicular to the opposite side. In parallelogram LMNP, LM is the base. PQ is an altitude drawn to LM. The formula to find the area of parallelogram LMNP may be derived as follows:
(figure available in print form)
(figure available in print form)
1. In ’ LMNP
draw altitude
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NR to LM extended.
2. NR = PQ
3. LP =MN
4.’ LQP Å ’ MRN
5. LQ = MR
6.’ LMNP = ’LQP+ Quad.QMNP
7 Rectangle QRNP = Quad
QMNP + ’ MRN
8. ’ LQP+Quad.QMNP= Quad.
QMNP + ’ MRN
9.
’
LMNP =Rectangle QRNP
10. LM = QR
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1. From a point outside a line exactly one line may be drawn I to the given line.
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2. 11 lines are everywhere equidistant.
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3. Opposite sides of a ’ are =.
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4. HL
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5. CPCTC
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6. Addition
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7. Reason 6
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8. Addition prop. of equality
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9.Substitution
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10.Reason 8
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11. Area of QRNP = QR x RN 11. Area of a rectangle = bh
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12. Area of LMNP = QR x RN 12. Substitution
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=LM x QP = bh
The area of a parallelogram equals the product of the base and an altitude drawn to that base. A =bh
(figure available in print form)
Example
: Find the area of parallelogram ABCD.
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Solution:
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First one must find the length of altitude CE.
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(CB)2 = (BE)2 + (CE)
2
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(10)2 = ( 6)2 + (CE)
2
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100 = 36 + (CE)
2
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64 = (CE)
2
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8 = CE
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A = bh = AB x CE = 24 x 8 = 192 square units
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Find the areas of the following parallelograms.
(figure available in print form)
