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...

Results 1 to 2 of 2

- January 30th 2010, 02:37 AM #1

- Joined
- Mar 2009
- From
- jharkhand
- Posts
- 77

## 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, 08:22 AM #2

- Joined
- May 2006
- From
- Lexington, MA (USA)
- Posts
- 11,814
- Thanks
- 703

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)