Question

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1. The area of trapezium is 34 cm² and the length of one of the parallel side is 10 cm and its height is 4 cm. Find the length of other parallel side.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{a}\mathrm{and}\mathrm{b}\mathrm{be}\mathrm{the}\mathrm{parallel}\mathrm{sides}\mathrm{of}\mathrm{trapezium}\mathrm{and}\mathrm{h}\mathrm{be}\mathrm{its}\mathrm{height}. \\ \mathrm{Now},\mathrm{a}=10\mathrm{cm};\mathrm{b}=?;\mathrm{h}=4\mathrm{cm} \\ \mathrm{Now},\mathrm{area}=34{\mathrm{cm}}^2 \\ \Rightarrow \frac{1}{2}\left(\mathrm{a}+\mathrm{b}\right)\mathrm{h}=34 \\ \Rightarrow \frac{1}{2}\left(10+\mathrm{b}\right)\times 4=34 \\ \Rightarrow 10+\mathrm{b}=17 \\ \Rightarrow \mathrm{b}=7 \\ \mathrm{So},\mathrm{other}\mathrm{parallel}\mathrm{side}\mathrm{is}\mathrm{of}\mathrm{length}7\mathrm{cm}. \end{gathered}$$