# How to find the height of an isosceles trapezoid given below, without the area?

Trapezoids are quadrilaterals with one set of parallel lines. They have many interesting properties and have many applications in the mathematical field.

## Answer: The height of the given trapezoid is 4 units.

Let's understand the steps to find the height of the given isosceles trapezoid without the area.

**Explanation:**

In the above figure, we are given the lengths of two parallel sides and one of the non-parallel sides.

Now, we mark the points on the trapezoid as shown in the figure below.

Then, we draw a perpendicular line from B to the line CD intersecting at O.

Hence, we have AB = 8, CD = 14 and AC = 5. We need to find height (h) AP.

First, we find the length of CP = (CD - OP - OD)

Now since the trapezoid is isosceles, we see that triangles APC and BOD are congruent. Hence, CP = OD.

Hence, length of CP = (CD - OP) / 2 = (14 - 8) / 2 = 3.

Now, using the Pythagoras theorem in triangle APC, we get

h = √(5^{2} - 3^{2}) = 4 units

### Thus, we found the height of the given isosceles trapezoid, without the area using the above steps. The height of the given trapezoid is 4 units.

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