Question

the area of a trapezium is 224 square and its height is 14 cm if one of the parallel side is longer than other by 8 cm find the length of two parallel sides​

Answer 1

A n s w e r

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G i v e n

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• Area of a trapezium is 224 sq. cm.

• Height is 14 cm.

• One parallel side is 8 cm longer than the other

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F i n d

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• The length of two parallel sides

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S o l u t i o n

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• Let the 2nd Parallel side be "x"

• Hence the 1st Parallel side is "x + 8"

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$\underline{\bold{\texttt{Area of trapezium :}}}$

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➠ $\sf \dfrac { 1 } { 2 } \times h \times (l_{1} + l_{2})$ ⚊⚊⚊⚊ ⓵

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Where ,

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• h = Distance between the parallel sides or height

• $\sf l_{1 }$ = 1st Parallel side

• $\sf l_{2}$ = 2nd Parallel side

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$\underline{\bold{\texttt{Area of given trapezium :}}}$

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• Area = 224 sq. cm.

• h = 14

• $\sf l_{1 }$ = x + 8 ⚊⚊⚊⚊ ⓶

• $\sf l_{2}$ = x

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⟮ Putting the above values in ⓵ ⟯

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➜ $\sf 224 = \dfrac { 1 } { 2 } \times 14 \times (x + 8 + x)$

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➜ $\sf 224 = 7 \times (x + 8 + x)$

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➜ $\sf \dfrac { 224 } { 7 } = 2x + 8$

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➜ $\sf 32 = 2x + 8$

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➜ $\sf 2x = 32 - 8$

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➜ $\sf 2x = 24$

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➨ $\sf x = 12$

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• Hence one parallel side is 12 cm

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⟮ Putting x = 12 in ⓶ ⟯

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➜ $\sf l_{1 }$ = x + 8

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➜ $\sf l_{1 }$ = 12 + 8

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➨ $\sf l_{1 }$ = 20

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• Hence the other parallel side is 20 cm

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∴ The parallel sides of trapezium are 12 cm & 20 cm

Answer 2

Question :

The area of a trapezium is 224 square and its height is 14 cm if one of the parallel side is longer than other by 8 cm find the length of two parallel sides.ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

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Given :

• Area of trapezium = 224cm²

• Height of trapezium = 14cm

To find :

• Length of two parallel sides.

Solution :

It's given that one of the parallel side is longer than other by 8 cm. So,

Let x be one one side.

Let Other side that is 8 cm longer.. = x+ 8

$\boxed {\tt Area \: of \: trapezium \: = \dfrac {1}{2} \times (sum \: of \: parallel \: sides) \times h }$

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$: \implies \tt { 224 = \dfrac {1}{2} \times {(x + x + 8)} \times 14 }$

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$: \implies \tt {224 = 7 \times (2x + 8)}$

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$: \implies \tt { \dfrac {224}{7} = 2x + 8}$

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$: \implies \tt { 32 = 2x + 8}$

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$: \implies \tt { x = 12 }$

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↬One side, x = 12cm

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↬other side, x + 8 = 12 + 8 = 20 cm