Question

The are of trapezium is 100 cm^2.If one parallel side is 12 cm. And height is 8 cm. Find the other parallel side

Answer 1

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$\huge{\bf{\green{\mathfrak{Question:-}}}}$

• The are of trapezium is 100 cm².If one parallel side is 12 cm. And height is 8 cm. Find the other parallel side.

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$\huge {\bf{\orange{\mathfrak{Answer:-}}}}$

• $\sf{Area\: of \:trapezium\: =\: 100 \:cm^{2}.}$

• $\sf{Height \: of \: the \: trapezium \: = \: 8 \: cm.}$

• $\sf{Length \: of \: one \: parallel \: side \: = \: a = \: 12 \: cm.}$

• $\boxed{\sf{Area \: of \: trapezium \: = \: \dfrac{a \: + \: b}{2} \: * \: h}}$

• $\sf{100 \: = \: \dfrac{12 \: + \: b}{2} \: * \: 8}$

• $\sf{\dfrac{100 \: * \: 2}{8} \: = \: 12 \: + \: b}$

• $\sf{\dfrac{200}{8} \: = \: 12 \: + \: b}$

• $\sf{25 \: = \: 12 \: + \: b}$

• $\sf{b \: = \: 25 \: - \: 12}$

• $\boxed{\therefore{\sf{b \: = \: 13 \: cm.}}}$

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$\huge{\bf{\red{\mathfrak{Conclusion:-}}}}$

• $\boxed{\therefore{\sf{Length \: of \: other \: parallel \: side \: = \: b \: = \: 13 \: cm.}}}$

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Answer 2

Given :-

Area of trapezium = 100 cm^2

One parallel side = 12 cm

Height = 8 cm

To Find :-

Length of 2nd parallel side

Solution :-

We know that

$\large \boxed {\sf Area = \dfrac{1}{2}\times\bigg (a + b\bigg) \times h}$

Let the other parallel side be x cm.

$\sf \implies 100 =\dfrac{1}{2} \bigg(12 + x\bigg) \times 8$

$\sf \implies 100 = 1 \bigg(12 + x \bigg) 4$

$\sf \implies 100 = 4\bigg(12 + x\bigg)$

$\sf \implies \dfrac{100}{4} = 12 + x$

$\sf \implies 25 = 12 + x$

$\sf \implies 25 - 12 = x$

$\sf \implies 13 = x\;\; \star$

Therefore :-

The length of other parallel side is 13 cm.