Find the missing height of the parallelogram when the area is 340 cm².

  17 cm

Step-by-step explanation:

The formula for the area of a parallelogram is ...

  A = bh

The base (b) is given as (5 cm +15 cm) = 20 cm. The area is given as 340 cm^2. Filling in the give numbers, we have ...

  340 cm^2 = (20 cm)h

Dividing by the coefficient of h gives ...

  (340 cm^2)/(20 cm) = h = 17 cm

The height of the parallelogram is 17 cm.

Comment on the geometry

The triangles at either end of the figure will be 5-12-13 right triangles, meaning the height of the figure is 12 cm. Using that height, we find the area to be (12 cm)(20 cm) = 240 cm^2 (not 340 cm^2). This leads us to believe there is a typo in the problem statement.

As the problem is given, the geometry is impossible. The height of the parallelogram cannot be greater than the length of the slanted side.

As the problem is written, it is a "one-step" problem. (Divide the area by the base length.) If the area were not given, then the Pythagorean theorem would be required to find the height. That is a 2-step problem:

  13^2 = 5^2 + h^2

  h^2 = 169 -25 = 144 . . . . solve for h²

  h = √144 = 12 . . . . . . . . . take the square root

It is not at all clear what 3 steps you're supposed to show in your work.