#### Question

The area of a trapezium is 1586 cm^{2} and the distance between the parallel sides is 26 cm. If one of the parallel sides is 38 cm, find the other.

#### Solution

Given:

Area of the trapezium = 1586 cm

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.

Area of the trapezium = 1586 cm

^{2}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.

Is there an error in this question or solution?

Solution 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. Concept: Area of Trapezium.