Geometry question PLEASE HELP!!!!

Question

There is a trapezoid that has an area of 25. If one of its bases is 4 and the other base is 6, what must its height be?

 

The given answer to this question is 20. I have worked it backwards using the formula and plugging the answer in and I am not getting 25 as an area for this problem. I isolated H to find the height setting the equation at 1/2(h)(6+4)=25. How is it possible for 20 to be the answer to this problem when either way it is worked, it makes no sense? 

 

 

PLEASE HELP!!! much details needed if its okay. Thank you!!!

Answer 1

A = (0.5)(b₁ + b₂)h

25 = (0.5)(4 + 6)h

50 = 10h

5 = h

 

It is the "given answer" that makes no sense. Textbooks have been known to contain errors (unlike the internet!).

Answer 2

The area of any trapezoid with base side lengths "b₁" and "b₂" and height "h" is given by the formula A = h(b₁ + b₂)/2.

 

The problem gives:

    A = 25 square units

    b₁ = 4 units

    b₂ = 6 units

 find h

 

Put values into the formula:

 

     25 = h(4+6)/2

     50 = 10h

      5 = h

 

Now, you checked  5(4+6)/2 = 25.  That's good.  Note that the area of a rectangle is base*height and the area of a trapezoid is (average base)*(height.  So, 5*5=25 checks out.

 

To get 20 as the height, using an average base of 5, the area must be 100 square units..

 

Good job !!     [note: you will also find typos and calculation errors on WyzAnt Answers Forum.]

Answer 3

A trapezoid has one pair of parallel sides.  Draw a transversal perpendicular to the two parallel sides.  The area of the trapezoid is equal to the length (which is the mean length of the two parallel sides) times the width (which is the part of the transversal between the parallel lines).

 

The two bases are 4 and 6, so the mean is 5.

If the area is 20, the width must be 20 / 5 = 4.

If the height is 20 and the bases are 4 and 6, the area would be 100.