Question

the area of trapezium is 400cm² the distance between the parallel sides is 16 cm if one of the parallel side is 20 cm find the length of the other ?​

Answer 1

Answer:

The length of the other parallel side is 30 cm

Step-by-step explanation:

We Have :-

Area of Trapezium = 400 cm²

Distance between the parallel sides = 16 cm

One of the parallel side = 20 cm

To Find :-

Length of the other parallel side

Formula Used :-

$Area \: of \: Trapezium \: = \: \dfrac{1}{2} \times ( \: sum \: of \: parallel \: sides \: ) \times height$

Solution :-

$400 = \dfrac{1}{2} \times (x + 20) \times 16 \\ \\ \dfrac{400 \times 2}{16} = x + 20 \\ \\ 50 = x + 20 \\ \\ x = 50 - 20 \\ \\ x = 30$

The length of the other parallel side is 30 cm

Answer 2

Answer:

$\large{\sf {\pmb{\underline{Given}}}}$

• ➥ The area of trapezium is 400cm²
• ➥ The distance between the parallel sides is 16 cm
• ➥ One of the parallel side of Trapezium is 20 cm.

$\begin{gathered} \: \: \end{gathered}$

$\large{ \sf {\pmb{\underline{To \: Find }}}}$

• ➥ The length of the other parallel side of Trapezium

$\begin{gathered} \: \: \end{gathered}$

$\large{ \sf{ \pmb{\underline{Using \: Formula}}} }$

$\underline{\boxed {\sf{Area \: of \: Trapezium = \dfrac{1}{2} \times ( Sum \: of \: Parallel \: side ) \times Height }}}$

$\begin{gathered} \: \: \end{gathered}$

$\large{\sf{ \pmb{\underline{Solution}}}}$

• ➠ Let the other side of Trapezium be "x" cm

  ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

According to the Question.

${ :\Rightarrow \: \sf \: Trapezium _{(Area)} = \dfrac{1}{2} \times (20 + x) \times 16 }$

$: \Rightarrow \: \sf {400 \: {cm}^{2} } = \dfrac{1}{2} \times (20 + x) \times 16 \:$

$:\Rightarrow \: \sf {400 } = \cancel \dfrac{16}{2} \times (20 + x)$

$:\Rightarrow \: \sf {400 } = 8 \times (20 + x)$

$:\Rightarrow \: \sf(20 + x) = \cancel \dfrac{400}{8}$

$:\Rightarrow \: \sf(20 + x) = 50$

$:\Rightarrow \: \sf{x = 50 - 20}$

$:\Rightarrow \: \sf{x = 30 \: m}$

$\: \: \large\underline {\boxed{\frak \purple{Base = 30 \: m}}}$

$\begin{gathered} \: \: \end{gathered}$

$\large{\sf{ \pmb{\underline{Verification }}}}$

${ :\Rightarrow \: \sf \: Trapezium _{(Area)} = \dfrac{1}{2} \times (a+ b) \times h }$

• Substituting the values

${ :\Rightarrow \: \sf 400 \: {cm}^{2} = \dfrac{1}{2} \times (20 + 30) \times 16}$

${ :\Rightarrow \: \sf 400 \: {cm}^{2} = \cancel\dfrac{16}{2} \times (50)}$

${ :\Rightarrow \: \sf 400 \: {cm}^{2} = (8 \: cm\times 50 \: cm)}$

${ :\Rightarrow \: \sf 400 \: {cm}^{2} =400 \: {cm}^{2} }$

$\: \: \large\underline {\boxed{\mathcal\purple{LHS =RHS }}}$

$\begin{gathered} \: \: \end{gathered}$

$\large{\sf{\pmb{\underline{Therefore}}}}$

• ➠ The length of the other parallel side of Trapezium is 30 cm.