Question

the area of a trapezium is 34cm², the length of one of the parellel side is 10cm and its height is 4cm. Find the length of the other parallel side.​

Answer 1

required question :

of a trapezium is 34 CM square the length of one of the parallel side is 10 cm and its height is 4 cm find the length of the other parallel side.

answer :

the height of the other parallel side is 7cm.

let's find out !!

given:

• area of trapezium = 34cm²
• length of one side of trapezium = 10cm
• height of trapezium = 4cm

using formula:

area of trapezium = ½ (a+b) ×h

so,

• =>> 34cm² = ½ (10+b) ×h

• =>> 34 × 2 ÷ 4 = 10 + b

• =>> 17 = 10+b

• =>> b = 10 -17

• =>> b = 7cm

hence the other side of trapezium is 7cm.

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related questions :-

question : -

area of a trapezium shaped field is 48m² the distance between two parallel side is 15m and one of the parallel side is 20m. find the other parallel side.

solution :-

one of the parallel side of a trapezium is a = 20 metre , let another parallel side be b , height h = 15m.

the given area of trapezium = 480m².

area of a trapezium = 480m².

so,

• 480m² = ½ (a+b) ×h

• 480 ×2÷15 = 20 + b

• 64 = 20 + b

• b = 44m

hence the other parallel side of the trapezium is 44m.

Answer 2

Answer:

Given

• :⇒ The area of Ttrapezium = 34cm²
• :⇒ The length of one of the parellel side = 10cm
• :⇒ The height of Trapezium = 4 cm

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To Find

• :⇒ Other parallel side of Trapezium

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Formula Used

${ : \Rightarrow\tt Area \: of \: Trapezium = \dfrac{1}{2} \times(Sum \: of \: parallel \: sides) \times Height }$

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Solution

Let the other side of Trapezium be "X" cm

So,

${ : \Rightarrow\tt 34 \: {cm}^{2} = \dfrac{1}{2} \times(10 + x) \times 4 }$

$\tt : \Rightarrow \dfrac{2 \times 34 \: {cm}^{2}} {4 \: cm} = (10 + x)$

$\tt : \Rightarrow \cancel\dfrac{68} {4} = (10 + x)$

$\tt : \Rightarrow (10 + x) = 17$

$\tt : \Rightarrow x = 17 - 10$

$\tt : \Rightarrow x = 7 \: cm$

$\Large \underline {\boxed{ \tt{Other \: Side = 7cm}}}$

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Verification

${ : \Rightarrow\tt Area \: of \: Trapezium = \dfrac{1}{2} \times(Sum \: of \: parallel \: sides) \times Height }$

${ : \Rightarrow\tt 34\: {cm}^{2} = \dfrac{1}{\cancel{2}} \times(10 + 7)cm \times \cancel{4}cm }$

${ : \Rightarrow\tt 34\: {cm}^{2} =(10 + 7)cm \times {2}cm }$

${ : \Rightarrow\tt 34\: {cm}^{2} =17 \: cm \times {2} \: cm }$

${ : \Rightarrow\tt 34\: {cm}^{2} =34\: {cm}^{2}}$

$\Large{\underline{\boxed{ \tt{LHS = RHS}}}}$

• Hence Verified.

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Therefore

The length of the other parallel side is 7 cm..