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Question
The area of a trapezium is 1586 cm2 and the distance between the parallel sides is 26 cm. If one of the parallel sides is 38 cm, find the other.
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Solution
Area of the trapezium = 1586 cm2
Distance between the parallel sides = 26 cm
And, length of one parallel side = 38 cm
Let us suppose the length of the other side to be x cm .
Now, area of the trapezium \[=\frac{1}{2}\times(\text{ Sum of the parallel sides })\times(\text{ Distance between the parallel sides })\]
\[ \Rightarrow 1586 =\frac{1}{2}\times(38+x)\times(26)\]
\[ \Rightarrow 1586=\frac{26}{2}\times(38+x)\]
\[ \Rightarrow 13\times(38+x)=1586\]
\[ \Rightarrow 38+x = \frac{1586}{13}=122\]
\[ \Rightarrow x = 122-38=84 cm\]
Hence, the length of the other parallel side is 84 cm.
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