Questions   
Sort: 
 #1
avatar+356 
+5
Jan 4, 2017
 #1
avatar+118651 
+11

An isosceles trapezoid has side lengths 13,4,13 and 14. What is the perimeter of its Varignon parallelogram?

 

I have decided to practice my descriptive skills.

It is important that you develope your comprehension skill in geometry descripions.  SO draw what I am describing and see if you can make sense of it.  If you cannot then ask and I will present some diagrams.  BUT if you try hard enough you probably will not need a diagram.

 

-----------

Draw the isosceles trapezoid so that the longest side is on the bottom of the pic

 

You will see that the diagonals of the varigon parallelogram cross at right angles.  So it is not just a parallelogram it is also a rhombus.  You only need to find one side because they are all the same.

 

If you cut your trapezium into three it is made up of a central rectangle  that is height by 4 units

and 2 congruent right angled triangles that are have a hypotenuse of 13 and one other side 5.

Using pythagoras's theorum it is easy to determine that the height is 12. This is the length of one of the diagonals.

 

Now consider the one of the congruent triangles.

Half the base is included in the other diagonal and the other half of it is not.  

The base is 5. so 2.5 is inincluded in the other diagonal.  But there are two right triangles so 2.5*2=5 units from the bas are NOT in the other diagonal.

So the diagonal is 14-5=9 units

 

So the two diagonals of the varignon rhomus are   9 and 12

The half diagonals are 4.5 and 6 units.

 

Using pythagoras again the legtn of the side of the rhombus will be 7.5 inits

So the perimeter will be 4*7.5 = 30units

Jan 4, 2017
Jan 3, 2017
 #1
avatar
0
Jan 3, 2017
 #4
avatar+561 
+6
Jan 3, 2017

3 Online Users

avatar
avatar