Question

The area of a trapezium is \[352c{{m}^{2}}\] and the distance between its parallel sides is \[16cm\]. If one of the parallel sides is of length \[25cm\], find the length of the other.

Answer 1

Hint: In this type of question we have to use the concept of finding areas of different geometrical shapes. We know that the formula for the area of trapezium is \[A=\dfrac{1}{2}\left( a+b \right)h\] where \[a\] and \[b\] are lengths of parallel sides and \[h\] is the distance between the parallel sides. We have given the distance between parallel sides and length of one of the parallel sides, by substituting these values in above formula and on simplification we can obtain the length of the other parallel side.

Complete step by step answer:
Now, we have to find the length of the other parallel side of the trapezium if the area of a trapezium is \[352c{{m}^{2}}\], the distance between its parallel sides is \[16cm\] and the length of the one of the parallel sides is \[25cm\].

Let us consider the formula for area of the trapezium which is given by,
\[\Rightarrow A=\dfrac{1}{2}\left( a+b \right)h\]
where \[a\] and \[b\] are lengths of parallel sides and \[h\] is the distance between the parallel sides.
By substituting the values \[A=352c{{m}^{2}},a=25cm,h=16cm\] in the above formula of area of trapezium we can write,
\[\begin{align}
  & \Rightarrow A=\dfrac{1}{2}\left( a+b \right)h \\
 & \Rightarrow 352=\dfrac{1}{2}\left( 25+b \right)\times 16 \\
\end{align}\]
On simplification we get,
\[\begin{align}
  & \Rightarrow 352=\left( 25+b \right)\times 8 \\
 & \Rightarrow \dfrac{352}{8}=\left( 25+b \right) \\
 & \Rightarrow 44=\left( 25+b \right) \\
 & \Rightarrow 44-25=b \\
 & \Rightarrow 19=b \\
 & \Rightarrow b=19cm \\
\end{align}\]
Hence, the length of the other parallel side of the trapezium is \[19cm\].

Note: In this type of question students have to note that trapezium is a type of quadrilateral in which two sides are parallel and two are non-parallel sides. Also students have to note that the distance between the parallel sides is also known as height of the trapezium.