Question

The area of a trapezium is 34 cm² and its height is 4 cm. One of the parallel sides of the trapezium is 10 cm, find the other parallel side​

Answer 1

Given: The area of a trapezium is 34 cm² & it's Height is 4 cm. also, one of the // side of the trapezium is 10 cm.

Need to find: The Length of other // side?

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❍ Let' say, that the other // side of the trapezium be x cm respectively.

As we know that,

⭒To calculate Area of Trapezium Formula Given by :

$\quad\star\:\;\underline{\boxed{ \bf{\frak{Area_{\:(trapezium)} = \dfrac{1}{2} \times \Bigg(a + b \Bigg) \times h}}}}$

where:

• a & b are the sides of the trapezium.
• h is the height of trapezium.
• & Area is given.

⠀

⠀$\underline{\bf{\dag} \:\mathfrak{Putting\;Values\;in\; formula\: :}}$⠀⠀⠀⠀

$\:\;\;:\implies\sf 34 = \dfrac{1}{\cancel{\;2}} \times \Bigg(10 + x\Bigg) \times \cancel{\;4} \\\\\\:\implies\sf 34 = \Bigg(10 + x\Bigg) \times 2\\\\\\:\implies\sf 34 = 20 + 2x\\\\\\:\implies\sf 34 - 20 = 2x\\\\\\:\implies\sf 14 = 2x\\\\\\:\implies\sf x = \cancel\dfrac{14}{2}\\\\\\:\implies\underline{\boxed{\pmb{\frak{x = 7 ~cm}}}}\;\bigstar$

$\therefore{\underline{\textsf{Hence, the length of other parallel side is \textbf{7 cm}.}}}$

Answer 2

Answer :-

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• Other parallel side of trapezium is 7 cm

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$\large\boxed{\textsf{\textbf{\pink{GIVEN\::-}}}}$

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• Area of a trapezium is 34 cm²

• Height of a trapezium is 4 cm

• One of the parallel sides of a trapezium is 10 cm

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$\large\boxed{\textsf{\textbf{\green{T0\:FIND\::-}}}}$

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• Other parallel side of trapezium?

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$\large\boxed{\textsf{\textbf{\blue{S0LUTI0N\::-}}}}$

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• Let us assume that other parallel side of a trapezium be s cm

• Using well known formula of area of trapezium ::

• $\tiny\underline{\boxed{\bf{\red{Area_{(trapezium)} = \dfrac{1}{2}\:\times\:\Big(Sum\:of\:parallel\:sides\Big)\:\times\:Height}}}}$

$\:$

$\underline{\sf{\bigstar\:Putting\:all\:known\:values\::-}}$

$\\ \qquad\dashrightarrow\:\sf 34 = \dfrac{1}{2}\:\times\:\Big(s + 10\Big)\:\times\:4$

$\\ \quad\dashrightarrow\:\sf 34 = \dfrac{\Big(s + 10\Big)\:\times\:\cancel{4}}{\cancel{2}}$

$\\ \qquad\dashrightarrow\:\sf 34 = \Big(s + 10\Big)\:\times\:2$

$\\ \quad\dashrightarrow\:\sf 34 = \Big[\big(s\:\times\:2\big) + \big(10\:\times\:2\big)\Big]$

$\\ \qquad\dashrightarrow\:\sf 34 = 2s + 20$

$\\ \quad\dashrightarrow\:\sf 34 - 20 = 2s$

$\\ \qquad\dashrightarrow\:\sf 14 = 2s$

$\\ \quad\dashrightarrow\:\sf s = {\cancel{\dfrac{14}{2}}}$

$\\ \qquad\dashrightarrow\:\underline{\boxed{\bf{\purple{ s = 7}}}}\:\bigstar$

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• Therefore, other parallel side of a trapezium is 7 cm

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$\large\boxed{\textsf{\textbf{\orange{M0RE\:T0\:KN0W\::-}}}}$

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$\underline{\sf{\bigstar\:Formulae\:of\:area\:of\:different\:shapes\::-}}$

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• Area of rectangle = Length × Breadth

• Area of square = (Side)²

• Area of circle = πr²

• Area of semi circle = ½ πr²

• Surface area of cube = 6 × (edge)²

• Surface area of cuboid = 2(lb + bh + hl)

• Surface area of cylinder = 2πr(r + h)

• Surface area of cone = πr(l + r)

• Surface area of sphere = 4πr²

• Surface area of hemi sphere = 3πr²

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