Question

Find the are of a trapezium whose parallel sides are 15 cm and 23 cm ; where as the non parallel sides are 10 cm and 8cm​

Answer 1

$\huge \underline \mathfrak\red{Question}$

Find the are of a trapezium whose parallel sides are 15 cm and 23 cm ; where as the non parallel sides are 10 cm and 8cm

$\huge \underline \mathfrak\green{Answer}$

DC = 15 cm , AB = 23 cm

AD = 10cm and BC = 8 cm

Draw CE parallel to DA which meets AB at point E .

since opposite sides of a quadrilateral AECD are parallel , it is a PARALLELOGRAM !

Also draw CF perpendicular to EB

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$\large \underline{ \rm \: In \: triangle \: \: EBC }$

Let a = EB = AB - AE = AB - DC = ( 23 - 15 ) cm = 8 cm

b = CE = DA = 10 cm and c = BC = 8cm

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$\rm{s = \dfrac{a + b + c}{2} = \dfrac{8 + 10 + 8}{2} = 13 \: cm}$

$\rm{ Area \: of \: </strong><strong>triangle</strong><strong> \: EBC = \sqrt{13(13-8)(13-10)(13-8)cm</strong><strong>^</strong><strong>2</strong><strong>} }$

$\rm{ = \sqrt{13 \times 5 \times 3 \times 5} cm</strong><strong>^</strong><strong>2</strong><strong>}=5 \sqrt{39} cm</strong><strong>^</strong><strong>2</strong><strong>$

$\boxed{ \implies5 \sqrt{39} }$

if CE is taken height corresponding to the base BE ,

then :-

$\rm{ \: Area \: of \:</strong><strong> </strong><strong>triangle</strong><strong> \: EBC= \dfrac{1}{2} ×EB×CF \: cm</strong><strong>^</strong><strong>2</strong><strong>}$

$\rm{ \dfrac{1}{2} \times 8 \times CF=5 \sqrt{39}} \implies{CF= \dfrac{5 \sqrt{39} }{4} cm}$

Clearly , distance between the parallel sides AB and DC is the length of CF .

AREA OF GIVEN TRAPEZIUM =

${ \rm{ \implies \dfrac{1}{2} ( \: sum \: of \: parallel \: sides \: ) \: \times \:( distance \: between \: them)}}$

$\rm{ \implies \: \dfrac{1}{2} (15 + 23) \times CF}$

$\rm{ \implies \: \dfrac{1}{2} \times 38 \times \frac{5 \sqrt{39} }{4} cm</u></strong><strong><u>^</u></strong><strong><u>2</u></strong><strong><u>=148.32 \: cm</u></strong><strong><u>^</u></strong><strong><u>2</u></strong><strong><u>}$

$\rm{Ans : - } \boxed { \rm\orange{ \implies \: Area \: of \: the \: given \: trapezium \: is \: 148.32 \: cm</u></strong><strong><u>^</u></strong><strong><u>2</u></strong><strong><u> }}$

$\boxed{ \rm{ \blue{@BrainlyBlockBuster}}}$