Question 238717
The old saying that a picture says a thousand words is no more appropriate than here!

First thing to do is draw the rectangle out with the mid points.

A______P______B
|**************|
|**************|
S**************Q
|**************|             
|**************|            
D______R______C

Then let's put down what we know about this rectangle:

AB = 2AD  (1)
2AB+2AD = 60  (2)

Subsituting in AB from (1) into (2) gives

2AB+AB = 60
3AB = 60

So we know AB = 20 units

So as we know P is halfway between A and B we know that AP = 10 units

S is halfway between AD so AS must be 5 units

We know that all the corner triangles APS, BPQ, CQR, DRS are equal in size so

The total area of the rectangle ABCD minus APS, BPQ, CQR and DRS must equal the area of the remaining quadrilateral PQRS.

Area of APS = 5*10*1/2 = 25 units

So the four triangles must have an area of 4*25 = 100

Rectangles area = AB*AD = 20*10 = 200

200 - 100 = 100 units

So PQRS = 100 units.

Does this make sense? I would suggest you draw it out for youself and go through each step to make sure you understand it.

James