Question

The area of a trapezium is 34 sq. cm and length of one of the parallel sides is 10 cm and its height is 4 cm. Find the length of the other parallel side​

Answer 1

${\tt{\red{\underline{\underline{\huge{Answer:= \: 7cm}}}}}}$

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$\LARGE{\bf{\underline{\underline\color{blue}{GIVEN:-}}}}$

• $\sf\green{ Area \: of \: Trapezium \: = \: 34cm²}$
• $\sf\green{ Length \: of \: the \: parallel \: side \: = \: a \: = \: 10cm}$
• $\sf\green{ Height \: = \: 4cm}$

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$\LARGE{\bf{\underline{\underline\color{purple}{Solution:-}}}}$

$\boxed{ \sf \blue{ Let\: the \: Length \: of \: other \: parallel \: side \: be \: b \: cm }}$

$\boxed{ \sf \orange{ Now, }}$

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\: Area \: of \: Trapezium \: = \: \frac{1}{2} \: ( \: a \: + \: b \: ) \: \times \: h }} }\\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \displaystyle \sf \: 34 \: = \: \frac{1}{2} \: ( \: 10 \: + \: b \: ) \: \times \: 4 \\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \displaystyle \sf \: 34 \: = \: \: ( \: 10 \: + \: b \: ) \: \times \: 2 \\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \displaystyle \sf \: 34 \: = \: 20 \: + \: 2b \: \\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \displaystyle \sf \: 34 \: - \: 20 = \: 2b \: \\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \displaystyle \sf \: 14 \: = \: 2b \: \\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \displaystyle \sf \: \frac{14}{2} \: = \: b \: \\ \\ \\\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}: \implies \underline{ \boxed{\displaystyle \sf \bold{\: 7 \: = \: b }} }\\ \\\end{gathered}\end{gathered}$

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$\sf\red{ So, \: length \: of \: other \: parallel \: side \: = \: 7cm}$

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Answer 2

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$\huge\mathtt \red{A} \blue{n} \pink{s} \purple{w} \blue{e} \orange{r}$

Gɪᴠᴇɴ

$Aʀᴇᴀ \: of \: trapezium \: = 34 cm \:^{2}$

Lᴇɴɢᴛʜ ᴏꜰ Oɴᴇ ᴘᴀʀᴀʟʟᴇʟ ꜱɪᴅᴇ

↬ a = 10

Hᴇɪɢʜᴛ (h ) = 4 cm

Lᴇᴛꜱ ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏꜰ ᴏᴛʜᴇʀ ᴘᴀʀᴀʟʟᴇʟ ꜱɪᴅᴇ of = b cm.

ɴᴏᴡ ,

Aʀᴇᴀ ᴏꜰ ᴛʀᴀᴘᴇᴢɪᴜᴍ

= 1/2 ( a + b) × h

↬ 34 = 1/2 ( 10 + b) × 4

↬ 34= ( 10 + b) × 2

↬ 34 = 20+ 2 b

↬ 34- 20 = 2 b

↬ 14 = 2 b

↬ 14 / 2 = b

↬ 7 = b

Length of the other parallel side is 7 cm.

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