Question

The area of a trapezium is 96 cm and its height is 8 cm. If one of the parallel side is longer than the other by 6 cm, then what is the length of the longer parallel side



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Answer 1

$\star \; {\underline{\boxed{\pmb{\red{\sf{ \; Given \; :- }}}}}}$

• Area of Trapezium = 96 cm²
• Height of Trapezium = 8 cm
• One parallel side is longer than other by 6 cm .

$\star \; {\underline{\boxed{\pmb{\green{\sf{ \; To \; Find \; :- }}}}}}$

• Length of longer parallel side = ?

$\star \; {\underline{\boxed{\pmb{\pink{\sf{ \; SolutioN \; :- }}}}}}$

$\maltese$ Formula Used :

• ${\underline{\boxed{\pmb{\sf{ Area{\small_{(Trapezium)}} = \dfrac{1}{2} \times \bigg(a + b \bigg) \times h }}}}}$

Where :

• a = 1st parallel side
• b = 2nd parallel side
• h = Height

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$\maltese$ According to the Question :

$\longmapsto$ Let the 2nd Parallel side be y .So,

$\qquad \; {\pmb{\sf{ 2nd \; Parallel \; Side = b = y \; cm }}}$

$\longmapsto$ 1st parallel side is 6 cm more than 2nd Parallel side .So,

$\qquad \; {\pmb{\sf{ 1st \; Parallel \; Side = a = y + 6 \; cm }}}$

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$\maltese$ Calculating the Value of y :

${\dashrightarrow{\qquad{\sf{ Area = \dfrac{1}{2} \times \bigg( a + b \bigg) \times h }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 96 = \dfrac{1}{2} \times \bigg\{ \bigg(y + 6 \bigg) + y \bigg\} \times 8 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 96 = \dfrac{1}{2} \times \bigg( 2y + 6 \bigg) \times 8 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 96 = \dfrac{1}{\cancel2} \times \bigg( 2y + 6 \bigg) \times \cancel8 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 96 = 1 \times \bigg( 2y + 6 \bigg) \times 4 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \dfrac{96}{4} = 2y + 6 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \cancel\dfrac{96}{4} = 2y + 6 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 24 = 2y + 6 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 24 - 6 = 2y }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 18 = 2y }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \dfrac{18}{2} = y }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \cancel\dfrac{18}{2} = y }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\pmb{\purple{\frak{ y = 9 }}}}}}}}$

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$\maltese$ Calculating the Sides :

• 1st Parallel side = y = 9 cm
• 2nd Parallel side = y + 6 = 9 + 6 = 15 cm

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$\maltese$ Therefore :

❛❛ Longer Parallel side of the Trapezium is 15 cm . ❜❜

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Answer 2

CONCEPT :

• first step we will apply the formula to calculate area of trapezium second step we will simplify the expression we will calculating the value x then, we will write the formula of trapezium then, we have to simplify with 96 , 8cm , 6 cm we get 9 third step Find length of parallel sides so, then, we get first parallel side and second parallel side
• Area of trapezium is given as A = 1/2 (Sum of parallel sides) × (Distance between them)

STEP 1 :

Given :

• the Area of trapezium is 96 cm²

• height is 8 cm

• one of the parallel side is longer than the other by 6 cm

Since one parallel side is longer than

other by 6 cm so let sides are x cm ,x + 6 cm respectively :

STEP 1 :

Apply formula to calculate area of trapezium

96 = 1/2 ( x + x + 6 ) × (8)

Step 2 :

Simplify the above expression

96 = ( 2x + 6 ) × 8 /2

2 x + 6 = 96 × 2 / 8

2 x + 6 = 24

2 x = 24 - 6

2 x = 18

x = 9

STEP 3 :

Find length of parallel sides

• So first parallel side is x = 9 cm

• And second parallel side is x + 6 = 9 + 6
• = 15

FINAL ANSWER :

• Hence, So first parallel side is 9 cm

• And second parallel side is 15 cm.