ABCD is a //gm, P is a point on BC such that BP:PC=1:2 and DP produced meets AB produced at Q. If area of △CPQ = 20 sq.cm, find:

1. area of △BPQ

2. area of △CPD

3. area of //gm ABCD.

pls. open the attached word document to view the figure...

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- January 30th 2010, 03:37 AM #1

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## Please help me with this simliarity sum..

ABCD is a //gm, P is a point on BC such that BP:PC=1:2 and DP produced meets AB produced at Q. If area of △CPQ = 20 sq.cm, find:

1. area of △BPQ

2. area of △CPD

3. area of //gm ABCD.

pls. open the attached word document to view the figure...

- January 30th 2010, 09:22 AM #2

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- Lexington, MA (USA)
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Hello, snigdha!

is a parallelogram.

Point is on such that: .

produced meets produced at

If area of , find:

1. area of

2. area of

3. area of parallelogramCode:D R C o - - - - - - - - - + - -o / * : / / * : / / * : / / * :/ / o P / /: * / / : * o - - - - - - - - - - - -o- + - - - - - o A B S Q

Draw line segment

. . Area of

Draw altitude through point

Since , then: .

. . That is: .

Area of

Area of

. . Hence: .

Then: .

Hence: . .(1)

We see that: .

. . and has twice the base and twice the height of

Hence: . .(2)

The area of is: .

Hence:. .

Note that: . = area of parallelgram

Therefore: .area of .(3)