# Find the area of shaded region

#### arangu1508

In the attached figure it is given ABCD is a rectangle and find the area of shaded region.

I am not able to solve this. Any clue or guidance please.

Thanks and regards

Aranga

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#### Cervesa

can you post a clean diagram with the correct orientation, please?

#### Cervesa

Are points B, O, and Q collinear?

#### arangu1508

Yes. It is collinear. Sorry. I am not able to get a clean copy. I am also not tech savvy so that to restore the original image.

Thanks.

#### WMDhamnekar

Area of the shaded region is 4.5.

arangu1508

#### Cervesa

$\Delta BSO \cong \Delta QRO$ by AAS $\implies |RO| = |OS|$

you should now be able to confirm the solution stated in post #5

arangu1508

#### arangu1508

I have one doubt whether the point O may vary? If the picture is not scaled.

#### Cervesa

if point O is not collinear with points B and Q, then I believe no conclusion of the shaded area can be reached ... that’s why I asked in post #3

arangu1508