How To Find The Height Of An Isosceles Trapezoid Without The Area ...

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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 = √(52 - 32) = 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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