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The area of the trapezium is 814 sq. cm and the lengths of the parallel sides 17 cm and 20 cm. Find the height of the trapezium.

Answer
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Hint: We are given that the length of parallel sides and area. We will substitute the values of area and length of parallel lines in the formula, $A = (½)\times\left( {a + b} \right)h$, where $a$ and $b$ are the length of the parallel sides of trapezium and $h$ is the height of the trapezium. We will then solve the equation to find the value of height.

Complete step-by-step answer:
We have the area of trapezium as 814 sq. cm.
The length of one of the parallel sides is 17 cm and the length of the other side is 20 cm.
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We have to find the area of the trapezium.
We know that the area of the trapezium is given by $A = (½)\times\left( {a + b} \right)h$, where $a$ and $b$ are the length of the parallel sides of trapezium and $h$ is the height of the trapezium.
On substituting the values of $a$, $b$ and area in the above formula, we get
$
  814 = (½)\times\left( {17 + 20} \right)h \\
   \Rightarrow 814 \times2= 37h \\
$
Divide both sides by 37.
$h = 44cm$
Here, the height of the trapezium is 44cm.
Note: Trapezium is a quadrilateral with one set of parallel lines and one set of non-parallel lines. The perpendicular distance between the parallel sides is the height of the trapezium. Area of any object is always measured in square units.