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In a parallelogram ABCD, if point P and Q are midpoints of AB and CD respectively and area of parallelogram ABCD = 16 $c m 2$ , then area of parallelogram APQD is ____ $c m 2$ .

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Detailed Solution

In a parallelogram ABCD, if point P and Q are midpoints of AB and CD respectively and area of parallelogram ABCD = 16

c m 2

, then area of parallelogram APQD is 8

c m 2

.
Given area of parallelogram ABCD = 16

c m 2

.

In a ||gm ABCD, if P and Q are midpoints of AB and CD respectively and ar(||gm ABCD) `= 16 cm^(2)` then ar(||gm APQD) = ? - Sarthaks eConnect | Largest Online Education Community

As, P and Q are mid-points of AB and CD respectively, therefore area of parallelogram APQD = area of parallelogram PBCQ. Area of parallelogram ABCD is,
A = Area of parallelogram APQD + Area of parallelogram PBCQ
A = 2 (Area of parallelogram APQD)
16 = 2 (Area of parallelogram APQD)
Area of parallelogram APQD is,

A= 162

A= 8cm 2

The area of parallelogram APQD is 8

cm 2

.

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