Altitude of a trapezoid... Did I get this right?

[HomeWork14]

Hello,
I wanted to know if I have the correct answer?
Thank You.

A Trapezoid has equal nonparallel sides, the upper base is 6 and the lower base is 16 ( 11 , 5), and the diagonal is 12. What is the altitude of the trapezoid? Round your answer to one decimal place.

My teacher hinted to use the pythagorean Theorem, so I did and ened up with this.
Is this correct?
Thank You :?:

Lower Base 16 ( 11,5)
11 ( squared) divided by 5(squared)
= 4.8 :?:

 

[soroban]

Hello, HomeWork14!

A trapezoid has equal nonparallel sides.
The upper base is 6, the lower base is 16, and the diagonal is 12.
What is the altitude of the trapezoid? .Round your answer to one decimal place.

We have trapezoid \(\displaystyle ABCD\) with \(\displaystyle AD\,=\,BC\).
We are given: \(\displaystyle \:AB\,=\,6,\;DC\,=\,16\).

From \(\displaystyle A\), drop perpendicular \(\displaystyle AE\) to side \(\displaystyle DC.\)
From \(\displaystyle B\), drop perpendicular \(\displaystyle BF\) to side \(\displaystyle DC.\)

Then: \(\displaystyle \:EF\,=\,6,\;DE\,=\,FC\,=\,5\).

            A     6     B
            * - - - - - *
           /|           |\
          / |           | \
         /  |           |  \
        /   |           |   \
       /    |           |    \
      * - - * - - - - - * - - *
      D  5  E     6     F  5  C

We are given diagonal \(\displaystyle BD\,=\,12\).
. . So the diagram looks like this:

            A     6     B
            * - - - - - *
           /         o  |\
          /   12  o     | \
         /     o        |h \
        /   o           |   \
       / o              |    \
      * - - - - - - - - * - - *
      D       11        E  5  C

In right triangle \(\displaystyle BED\), we have: \(\displaystyle \:h^2\,+\,11^2\:=\:12^2\)

Solve for \(\displaystyle h\).