- #1

zaldar

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expect I am going to have to skip ones like this during the test but thought I would get help with them anyway just for learning from the engineers here. Also putting both problems here in one post, hope that is ok.

Problem 1 15 in problem150002.pdf

Quantitative comparison problems you have a square PRSU and a parallelogram drawn inside the square, PQ ST such that q and t are midpoints of opposite sides of the square. (file with picture attached). You know one side of the parallelogram (SQ) equals the square root of five. Question is how does the area of the region PQST compare with 3/2.

Not sure honestly...

Thought that you could use a 45 45 90 triangle as the lines to the midpoints would bisect the the 90 degree angle, quickly became obvious though that this was nonsensical as then tu would equal pu. Tried putting in a line QT making a rectangle on the bottom of the square but that didn't seem to help much either.

Problem 2 29 in problem 290003.pdf

Mostly looking for hints on how to do problems like this more quickly and without a calculator. I could do this one but it would take me ten minutes or so which on the GRE is not a good idea.

You have an octagon with alternating sides of square root of 2 and 1 and you know that the octagon is equiangular. They want you to find the area of the polygon.

You need to find the perimeter (which is easy for this one) and the apothem. You can find the angle measure using (180n-360)/n

You can draw a right triangle from the corners and then use the properties of triangles to find the length of the apothem but you are not given any kind of radius (the geometry book I have gives that on the problems I found to practice) which makes the problem even more time consuming. Any tricks here appreciated!

Lastly a general question, is it always true that the height of a parallelogram is less than the length of the longest side or is that only true in certain circumstances?

Ok thanks, now to go see if there is a chemistry question I can help someone with or an algebra one.

Problem 1 15 in problem150002.pdf

## Homework Statement

Quantitative comparison problems you have a square PRSU and a parallelogram drawn inside the square, PQ ST such that q and t are midpoints of opposite sides of the square. (file with picture attached). You know one side of the parallelogram (SQ) equals the square root of five. Question is how does the area of the region PQST compare with 3/2.

## Homework Equations

Not sure honestly...

## The Attempt at a Solution

Thought that you could use a 45 45 90 triangle as the lines to the midpoints would bisect the the 90 degree angle, quickly became obvious though that this was nonsensical as then tu would equal pu. Tried putting in a line QT making a rectangle on the bottom of the square but that didn't seem to help much either.

Problem 2 29 in problem 290003.pdf

Mostly looking for hints on how to do problems like this more quickly and without a calculator. I could do this one but it would take me ten minutes or so which on the GRE is not a good idea.

## Homework Statement

You have an octagon with alternating sides of square root of 2 and 1 and you know that the octagon is equiangular. They want you to find the area of the polygon.

## Homework Equations

You need to find the perimeter (which is easy for this one) and the apothem. You can find the angle measure using (180n-360)/n

## The Attempt at a Solution

You can draw a right triangle from the corners and then use the properties of triangles to find the length of the apothem but you are not given any kind of radius (the geometry book I have gives that on the problems I found to practice) which makes the problem even more time consuming. Any tricks here appreciated!

Lastly a general question, is it always true that the height of a parallelogram is less than the length of the longest side or is that only true in certain circumstances?

Ok thanks, now to go see if there is a chemistry question I can help someone with or an algebra one.