Question

The area of a trapezium field is 960 m2

, the distance between two parallel sides is 30 m and

one of the parallel side is 44 m. Find the other parallel side.​

Answer 1

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$\LARGE\mathfrak{\underline{\underline\textcolor{aqua}{✯\; Given :-}}}$

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$\qquad\tt{:}\longrightarrow\large\textsf{Area of the Trapezium field = 960 m²}$

$\qquad\tt{:}\longrightarrow\large\textsf{Distance between two parallel sides ( h ) = 30m}$

$\qquad\tt{:}\longrightarrow\large\textsf{Length of one parallel side = 44m}$

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$\LARGE\mathfrak{\underline{\underline\textcolor{aqua}{✯\; To \; \; Find :-}}}$

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$\qquad\tt{:}\longrightarrow\large\textsf{Length of the other parallel side = ?}$

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$\LARGE\mathfrak{\underline{\underline\textcolor{aqua}{✯\; Formula :-}}}$

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$\qquad\tt{:}\Longrightarrow{\boxed{\large\textsf\textcolor{purple}{ {\large\textsf{Area}}_{\large\textsf{( \; Trapezium \; )}} } \large\textsf\textcolor{purple}{ = \cfrac{\large\textsf{1}}{\large\textsf\textcolor{purple}{2}} }\large\textsf\textcolor{purple}{× ( A + B ) × h}}}$

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• A = One parallel side
• B = Another parallel side
• h = Distance between the two parallel sides

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$\LARGE\mathfrak{\underline{\underline\textcolor{aqua}{✯\; Solution :-}}}$

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$\qquad\tt{:}\longrightarrow\large\textsf{ {\large\textsf{Area}}_{\large\textsf{( \; Trapezium \; )}} } \large\textsf{ = \cfrac{\large\textsf{1}}{\large\textsf{2}} }\large\textsf{× ( A + B ) × h}\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{ 960 = \cfrac{\large\textsf{1}}{\large\textsf{2}} \large\textsf{× ( 44 + B ) × 30}}\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{ \cfrac{\large\textsf{960 × 2}}{\large\textsf{30}} = \large\textsf{44 + B } }\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{ \cancel\cfrac{\large\textsf{1920}}{\large\textsf{30}} = \large\textsf{44 + B } }\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{64 = 44 + B}\\\\\\\qquad\tt{:}\longrightarrow\large\textsf{64 - 44 = B}\\\\\\\qquad\tt{:}\longrightarrow\boxed{\large\mathfrak\textcolor{red}{20 = B }}$

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$\qquad\large\textsf\textcolor{orange}{∴ The other parallel side = 20m}$

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* To get the given solution in more detail refer to the above attachment :)

Answer 2

${\rm{\red{\underline{\underline{Given : }}}}}$

• Area of trapezium shaped field is 448 m².

• Distance between the parallel sides is 14m.

• One of the parallel sides is of 44m.

${\rm{\blue{\underline{\underline{To \: Find: }}}}}$

The measure of the other parallel side.

${\rm{\green{\underline{\underline{Formula \: Used: }}}}}$

$\rm Area \: of \: trapezium = \frac{sum \: of \: parallel \: sides \: }{2} \times height$

Let's denote the parallel sides by $d_{1}$ and $d_{2}$ where, $d_{1}$ is 44m

Now formula becomes :-

$\rm Area \: of \: trapezium = \frac{ d_{1} + d_{2} }{2} \times height$

Here, height is the distance between the parallels.

${\rm{\orange{\underline{\underline{Calculations : }}}}}$

Let the second parallel side $(d_{2} )$ be x m.

$\rm Area \: of \: trapezium = \frac{ d_{1} + d_{2} }{2} \times height$

Substituting the values,

$\longrightarrow\rm 448 = \frac{44 + x}{2} \times 14$

$\longrightarrow\rm 448 = \frac{44 + x}{ \cancel2} \times \cancel{14}$

$\longrightarrow\rm 448 = 44 + x \times 7$

$\longrightarrow\rm \frac{448}{7} = 44 + x$

$\longrightarrow\rm \frac{ \cancel{448}}{\cancel7} = 44 + x$

$\longrightarrow\rm 64 = 44 + x$

$\longrightarrow\rm x = 64 - 44$

$\longrightarrow\rm x = 20 \: metres$

Hence, the other parallel is of 20 metres.