Thread: Question on Similarity

Doc1.doc
The diagram is attached.
The question is:
In the diagram is a parallelogram. If , and the area of , find the area of triangle .

The area of a parallelogram is "height times base". Since you are told that the base (the length of AD which is the same as the length of BC) is 4 and that the area of the parallelogram is 40, the height, the perpendicular distance from BC to AD, is 10.

The area of a triangle is "(1/2) heigth times base" and the base of triangle APD is also 4 so you need to find the perpendicular distance from P to AD. That will be 10 plus the perpendicular distance from P to BC. The two right triangles having hypotenuses CP and DC are similar triangles but, since you do not know CD, I see no way of using that to get the perpendicular distance you need.

Originally Posted by HallsofIvy

The area of a parallelogram is "height times base". Since you are told that the base (the length of AD which is the same as the length of BC) is 4 and that the area of the parallelogram is 40, the height, the perpendicular distance from BC to AD, is 10.

The area of a triangle is "(1/2) heigth times base" and the base of triangle APD is also 4 so you need to find the perpendicular distance from P to AD. That will be 10 plus the perpendicular distance from P to BC. The two right triangles having hypotenuses CP and DC are similar triangles but, since you do not know CD, I see no way of using that to get the perpendicular distance you need.

To get a triangle as APD, a new line segment will have to be made. Can you please explain, 'the perpendicular distance from P to AD. That will be 10 plus the perpendicular distance from P to BC.' ?

I too tried a lot to get something helpful...but did not get any. There is possibly no way to answer your question...

Originally Posted by Ilsa

To get a triangle as APD, a new line segment will have to be made. Can you please explain, 'the perpendicular distance from P to AD. That will be 10 plus the perpendicular distance from P to BC.' ?

Yes, and that new line segment is the line from P perendicular to line AD. The length of that line segment is 'the perpendicular distance from P to AD'. The length of the line segment from P to perpendicular BC is the second "perpendicular distance".