Question

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 1

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.

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.