# In isosceles trapezoid HJKL, HJ ll LK. Suppose that points M,N,P, and Q are midpoints of the sides HL,HJ,JK, and LK. If the length of diagonal HK is 10 cm, find the perimeter of MNPQ.

*print*Print*list*Cite

Expert Answers

tiburtius | Certified Educator

We will use the following theorem:

*Line segment which connects midpoints of two sides of a triangle is parallel to the third side and is half of the length of the third side.*

Let's first look at triangle HJK, in it the line segment NP connects two of the triangles sides midpoints and since the third side of the triangle is HK=10cm it follows that NP=5cm.

Similarly from triangle HKL we get QM=5cm.

Since this is isosceles trapezoid it follows that both of its diagonals are equal i.e. HK=JL=10cm. Now from triangles HJL and JKL we get MN=5cm and PQ=5cm.

We can now calculate perimeter of MNPQ.

`P_(MNPQ)=|MN|+|NP|+|PQ|+|QM|`

`P_(MNPQ)=5+5+5+5=20"cm"`