Question

The area of trapezium is \[480{m^2}\], the distance between two parallel sides is 15 cm and one parallel side is 20 cm. Find another parallel side?
A. 44 cm
B. 42 cm
C. 43 cm
D. None of these

Answer 1

Hint: As we know that, area of trapezium = $\dfrac{1}{2} \times h \times \left( {sumofparallelsides} \right)$ and the distance between two parallel sides of trapezium and can be considered as it’s height . Here in the question, it is mentioned that one side is \[20cm\]. Hence, we can calculate one unknown quantity as rest all we know in the equation.

Complete step by step Answer:

Diagram:

Let one parallel side be x.
Given that area of trapezium is\[480{m^2}\]and \[h = 15{\text{ }}cm\] (h = distance between parallel side)
Now putting the values in the formula of area of trapezium ,
\[480 = {\text{ }}\dfrac{1}{2}{\text{ }}h\left( {sum{\text{ }}of{\text{ }}parallel{\text{ }}side} \right)\]
\[480 = \dfrac{1}{2}\left( {15} \right)\left( {x + 20} \right)\] …(1)
On solving (1) , and simplifying it further
\[960 = \left( {15} \right)\left( {x + 20} \right)\]
\[64 = \left( {x + 20} \right)\]
\[x = 44{\text{ }}cm\]
Thus, length of another parallel side of trapezium is $44cm$
Hence, option (A) is correct answer.

Note: A trapezium is a Quadrilateral having 2 parallel sides and the other 2 sides are not parallel. The diagonals of regular trapezium bisect each other. In a trapezium, the length of the mid-segment is equal to half the sum of parallel bases.