Given: AKLM is a trapezoid, AK=13 LM=14, KL=5, AM=20 Find: h

The height of the trapezoid is

Explanation:

AKLM is a trapezoid.

The measurements of the trapezoid are AK=13, LM=14, KL=5, AM=20

We need to find the height of the trapezoid.

Let M' be a point on AM that is 5 units toward point A from M.

Let B be a point on AM such that KB⊥AM. Let x = AB; then BM' = 15 -x.

Using Pythagorean theorem, we have,

--------(1)

-----------(2)

Subtracting the two equations, we have,

Simplifying, we get,

Subtracting both sides of the equation by 225, we get,

Dividing by 30, we get,

Substituting in the equation , we get,

Thus, the height of the trapezoid is