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1) P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar (APB) = ar(BQC).
2) ABCD is a parallelogram, AE perpendicular to DC and CF perpendicular AD.If AB = 16 cm, AE= 8cm and CF = 10cm, find AD. diagram
1) P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar (APB) = ar(BQC).
2) ABCD is a parallelogram, AE perpendicular to DC and CF perpendicular AD.If AB = 16 cm, AE= 8cm and CF = 10cm, find AD. diagram
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Answer:
If a triangle and a parallelogram are on the same base and between the same parallel lines, the area of the triangle will be half of the area of the parallelogram.
P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar (APB) = ar (BQC)
It can be observed that ΔBQC and parallelogram ABCD lie on the same base BC and these are between the same set of parallel lines AD and BC.
∴ Area (ΔBQC) = 1/2 Area (ABCD).....(1)
Similarly, ΔAPB and parallelogram ABCD lie on the same base AB and between the same set of parallel lines AB and DC.
∴ Area (ΔAPB) = 1/2 Area (ABCD).....(2)
From Equations (1) and (2), we see that,
Area (ΔBQC) = Area (ΔAPB)
Step-by-step explanation:
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