Question

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$\huge{\underline{\mathrm\pink{\fcolorbox{white}{white}{Question:-}}}}$



area of trapezium of height 4 cm is 32 cm^2 One of the parallel sides of the trapezium is cm. Find the length of the other parallel side !!

Answer:
$\huge \fbox \colorbox{orange}{Don't~Spam࿐ }$​

Answer 1

Convenient Question :-

›»› Area of trapezium of height 4 cm is 32 cm². One of the parallel sides of the trapezium is 10 cm. Find the length of the other parallel side.

Answer :-

›»› The length of the other parallel sides of a trapezium is 6 cm.

Explanation :

$\huge\bold{Given :}$

• Area of trapezium = 32 cm².

• Height of a trapezium = 4 cm.

• One of the parallel sides of a trapezium = 10 cm.

$\huge\bold{To~find:}$

• Length of the other parallel sides of a trapezium = ?

$\huge\bold{Solution :}$

Let us assume that, other parallel sides of a trapezium is x cm.

We know that, if we are given with the area of trapezium, height of a trapezium and one of the parallel sides of a trapezium then we have the required formula, that is,

→ Area of trapezium = 1/2 * (sum of parallel sides) * height.

Substituting all the given values in the formula, we get :

→ 32 = 1/2 * (10 + x) * 4

→ 32 = 1 * (10 + x) * 2

→ 32 = 1 * (10 + x) * 2

→ 32 = (10 + x) * 2

→ 32/2 = 10 + x

→ 16 = 10 + x

→ 16 - 10 = x

→ x = 6

Hence, the length of the other parallel sides of a trapezium is 6 cm.

Verification :

→ Area of trapezium = 1/2 * (sum of parallel sides) * height

→ 32 = 1/2 * (10 + 6) * 4

→ 32 = 1/2 * 16 * 4

→ 32 = 1 * 8 * 4

→ 32 = 8 * 4

→ 32 = 32

$\huge{\underline{\mathcal\pink{\fcolorbox{red}{blue}{Hence,~verified !! }}}}$

Answer 2

Answer :-

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Question\;:-}}}$

Here the concept of Areas of Trapezium has been used. We are given the dimensions of the Trapezium. Its area is half the product of sum of parallel sides of Trapezium multiplied by perpendicular distance between them. We are given the height, area and one parallel side. We can apply the value and find the answer.

Let's do it !!

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★ Formula Used :-

$\\\;\boxed{\sf{Area\;of\;Trapezium\;=\;\bf{\dfrac{1}{2}\;\times\;(Sum\;of\;Parallel\;Side)\;\times\;Distance\;Between\;them}}}$

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★ Correct Question :-

Area of trapezium of height 4 cm is 32 cm².One of the parallel sides of the trapezium is 6 cm. Find the length of the other parallel side.

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★ Solution :-

Given,

» Perpendicular distance between the parallel sides of the Trapezium = height = 4 cm

» Area of the Trapezium = 32 cm²

» One of the Parallel side = 6 cm

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~ For the length of other Parallel sides of Parallelogram ::

• Let the other parallel side of the Trapezium be x .

Then,

$\\\;\;\;\sf{:\mapsto\;\;Area\;of\;Trapezium\;=\;\bf{\dfrac{1}{2}\;\times\;(Sum\;of\;Parallel\;Side)\;\times\;Distance\;Between\;them}}$

$\\\;\;\;\sf{:\mapsto\;\;32\;=\;\bf{\dfrac{1}{2}\;\times\;(6\;+\;x)\;\times\;4}}$

By transposing this to other side, we get,

$\\\;\;\;\sf{:\mapsto\;\;(6\;+\;x)\;=\;\bf{\dfrac{32\;\times\;2}{4}}}$

$\\\;\;\;\sf{:\mapsto\;\;(6\;+\;x)\;=\;\bf{8\;\times\;2}}$

$\\\;\;\;\sf{:\mapsto\;\;(6\;+\;x)\;=\;\bf{16}}$

$\\\;\;\;\sf{:\mapsto\;\;x\;=\;\bf{16\;-\;6}}$

$\\\;\;\;\bf{:\mapsto\;\;x\;=\;\bf{10\;\;cm}}$

$\\\;\large{\underline{\underline{\rm{Hence,\;length\;of\;other\;side\;is\;\;\boxed{\bf{10\;\;cm}}}}}}$

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$\qquad\quad\boxed{\bf{\mid{\overline{\underline{\purple{\bigstar\: More \: to \; know \: :}}}}}\mid}$⠀

$\\\;\sf{\leadsto\;\;Area\;of\;Rectangle\;=\;Length\;\times\;Breadth}$

$\\\;\sf{\leadsto\;\;Area\;of\;Square\;=\;(Side)^{2}}$

$\\\;\sf{\leadsto\;\;Area\;of\;Circle\;=\;\pi r^{2}}$

$\\\;\sf{\leadsto\;\;Area\;of\;Triangle\;=\;\dfrac{1}{2}\;\times\;Base\;\times\;Height}$

$\\\;\sf{\leadsto\;\;Area\;of\;Parallelogram\;=\;Base\;\times\;Height}$

$\\\;\sf{\leadsto\;\;Perimeter\;of\;Rectangle\;=\;2\;\times\;(Length\;+\;Breadth)}$

$\\\;\sf{\leadsto\;\;Perimeter\;of\;Cube\;=\;2\;\times\;(Side)}$

$\\\;\sf{\leadsto\;\;Perimeter\;of\;Circle\;=\;2\pi r}$