Question

yge area of trapezium sheped felled is 480m², the distqnxw between two parell side is 15m and one of tge parallel side is 20m ,find the other side​

Answer 1

$\displaystyle\large\underline{\sf\red{Given}}$

✭ Area of a Trapezium is 480 m²

✭ Distance between the two parallel sides(height) = 15 m

✭ One of the parallel side = 20 m

$\displaystyle\large\underline{\sf\blue{To \ Find}}$

◈ The other side?

$\displaystyle\large\underline{\sf\gray{Solution}}$

So we know that area of a Trapezium is given by,

$\displaystyle\sf\underline{\boxed{\sf \dfrac{Sum \ of \ parallel \ sides}{2} \times Height}}$

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$\displaystyle\sf\underline{\boldsymbol{\bullet \: According \ to \ the \ Question}}$

• Parallel sides are of length x & 20 m
• Height of the figure is 15 m
• Area is 480 m²

$\displaystyle\sf\dashrightarrow \dfrac{20+x}{2} \times 15 = 480$

$\displaystyle\sf\dashrightarrow \dfrac{20+x}{2} = \dfrac{480}{15}$

$\displaystyle\sf\dashrightarrow \dfrac{20+x}{2} = 32$

$\displaystyle\sf\dashrightarrow 20+x = 32\times 2$

$\displaystyle\sf\dashrightarrow 20+x = 64$

$\displaystyle\sf\dashrightarrow x = 64-20$

$\displaystyle\sf\pink{\dashrightarrow x = 44 \ m}$

$\displaystyle\sf\therefore The \ other \ parallel \ side \ is \ 44 \ m$

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Answer 2

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

◕ Area of trapezium shaped shaped field = 480 m²

◕ Distance between two parallel lines i.e., Height = 15 m

◕ One of the parallel side = 20 m

$\red{\large{\underline{\underline{ \rm{To \: Find: }}}}}$

◉ The other parallel side.

$\red{\large{\underline{\underline{ \rm{Solution: }}}}}$

Let the other parallel side be x.

We know, the area of the trapezium is given by:

Formula for Area of a trapezium:

$\green{ \underline{ \boxed{ \rm{</u></strong><strong><u>A</u></strong><strong><u>rea = \frac{1}{2} \times (sum \: of \: parallel \: sides) \times height}}}}$

We have,

$480 = \frac</u></strong><strong><u>{</u></strong><strong><u>1</u></strong><strong><u>}</u></strong><strong><u>{</u></strong><strong><u>2</u></strong><strong><u>}</u></strong><strong><u> </u></strong><strong><u>\</u></strong><strong><u>t</u></strong><strong><u>i</u></strong><strong><u>m</u></strong><strong><u>e</u></strong><strong><u>s</u></strong><strong><u> </u></strong><strong><u>(</u></strong><strong><u>20 + x</u></strong><strong><u>)</u></strong><strong><u> \times 15$

$480 \times 20 = (20 + x) \times 15$

$960 = (20 + x) \times 15$

$\frac{960}{15} = 20 + x$

$64 = 20 + x$

$x = 64 - 20$

$x = \rm44 \: cm$

∴ The other parallel side = $\green{ \underline{ \boxed{ \rm{44 \: cm}}}}$

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