Question

The height of the trapezium whose area is 200 sq cm and the sum of parallel sides is 25 cm
is __________.

Answer 1

Given : The area of of atrapezium is 200cm² & the sum of Parallel side is 25 cm .

Exigency to find : The Height  ofTrapezium .

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❍ Let the altitude of the trapezium be h cm respectively.

⠀⠀⠀$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

$\star\;{\boxed{\sf{\pink{Area_{\;(trapezium)} = \bigg( \dfrac{1}{2}\times h\times (a+b)\bigg)}}}}$

Where,

• a + b is the sum of the two parallel sides and h is distance between two parallel sides or height of trapezium.⠀

⠀⠀⠀

⠀⠀⠀⠀⠀⠀$\underline {\frak{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

$:\implies\sf 200 = \dfrac{1}{2}\times25 \times h \\\\\\:\implies\sf 200 \times 2 = 25\times h \\\\\\:\implies\sf 400 = 25 \times h \\\\\\ :\implies\sf 400 = 25h\\\\\\:\implies\sf 400 = 25h \\\\\\:\implies\sf h = \cancel\dfrac{400}{25}\\\\\\:\implies{\underline{\boxed{\frak{\pink{h = 16\;cm}}}}}\;\bigstar$

$\therefore{\underline{\sf{Hence, \;the\;Height \; of \;Trapezium \;is\;\bf{ 16\;cm}.}}}$

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V E R I F I C A T I O N :

⠀⠀⠀$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

$\star\;{\boxed{\sf{\pink{Area_{\;(trapezium)} = \bigg( \dfrac{1}{2}\times h\times (a+b)\bigg)}}}}$

Where,

• a + b is the sum of the two parallel sides and h is distance between two parallel sides or height of trapezium.⠀

⠀⠀⠀

⠀⠀⠀⠀⠀⠀$\underline {\frak{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

$:\implies\sf 200 = \dfrac{1}{2}\times25 \times 16 \\\\\\:\implies\sf 200 = \dfrac{1}{\cancel {2}}\times25 \times \cancel {16} \\\\\\ :\implies\sf 200 = 25 \times 8 \\\\\\:\implies\bf 200 cm²= 200 cm²$

⠀⠀⠀⠀⠀$\therefore {\underline {\bf{ Hence, \:Verified \:}}}$

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