Question

The area of a trapezium is 850 sq. cm. One of the parallel sides is 64 cm and the
perpendicular distance between the parallel sides is 17 cm. Find the length of
other parallel side.
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Answer 1

GIVEN :-

• The area of trapezium = 850 m².
• One parallel side , a = 64 cm.
• Height , h = 17 cm.

TO FIND :-

• The other parallel side , b.

SOLUTION :-

★ Area of Trapezium = 1/2 (a + b) × h.

Substitute all the values,

➼ 850 = 1/2 (64 + b) × 17

➼ 850 = 1/2 (64 + b) × 17.

➼ (850 × 2)/17 = 64 + b

➼ 1700/17 = 64 + b

➼ 100 = 64 + b

➼ b = 100 - 64

➼ b = 36

❏ Hence The other parallel side is 36 cm.

★ VERIFICATION ★

★ Area of Trapezium = 1/2 (a + b) × h.

Substitute all the values,

➼ 850 = 1/2 (64 + 36) × 17

➼ 850 = 32 + 18 × 17

➼ 850 = 50 × 17

➼ 850 = 850

L.H.S = R.H.S

❏ HENCE VERIFIED.

Answer 2

ANSWER ✔

$\large\underline\bold{GIVEN,}$

$\sf\dashrightarrow area\:of\:TRAPEZIUM= 850cm^2$

$\sf\dashrightarrow parallel\:side\:of\:trapezium\:(a)= 64cm$

$\sf\dashrightarrow distance\:between\:parallel\:sides(height)=17cm$

$\large\underline\bold{TO\:FIND,}$

$\sf\dashrightarrow THE\:LENGTH\:OF\:THE\:OTHER\:PARALLEL \:SIDE$

✯FORMULA IN USE,

$\large{\boxed{\bf{ area\:of\:trapezium=\dfrac{1}{2} \times (sum\:of\:parallel\:sides) \times height.}}}$

$\large\underline\bold{SOLUTION,}$

$\sf\therefore area\:of\:trapezium=\dfrac{1}{2} \times (a+b) \times height$

$\sf\implies 850= \dfrac{1}{2} \times (64+b)\times 17$

$\sf\implies 850 \times 2= (64+b) \times 17$

$\sf\implies 1700= (64+b) \times 17$

$\sf\implies \dfrac{1700}{17}= 64+b$

$\sf\implies \cancel\dfrac{1700}{17}= 64+b$

$\sf\implies 100=64+b$

$\sf\implies 100-64=b$

$\sf\implies 36=b$

$\large{\boxed{\bf{ \star\:\: b=36\:\: \star}}}$

$\large\underline\bold{THE\: LENGTH\:OF\:THE\:OTHER\: PARALLEL\:SIDE\:IS\:36cm}$

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