Question

The Area of trapezium of height 24.2 cm is 605 cm².one of the parrallel sides is 21 cm,find the other side.​

Answer 1

Given :

• Area of trapezium of height 24.2 cm is 605 cm².
• Length of one parallel side is 21 cm .

To Find :

• Length of other parallel side .

Solution :

$\longmapsto\tt{Parallel\:Side=21\:cm\:and\:x\:cm}$

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Trapezium=\dfrac{1}{2}\times{(Sum\:of\:parallel\:sides)}\times{h}}$

Putting Values :

$\longmapsto\tt{605=\dfrac{1}{2}\times{(21+x)}\times{24.2}}$

$\longmapsto\tt{605\times{2}=508.2+24.2x}$

$\longmapsto\tt{1210-508.2=24.2\:x}$

$\longmapsto\tt{701.8=24.2\:x}$

$\longmapsto\tt{x=\dfrac{7018\times{\cancel{{10}}}}{242\times{{\cancel{10}}}}}$

$\longmapsto\tt{x=\cancel\dfrac{7018}{242}}$

$\longmapsto\tt\bf{x=29\:cm}$

So , The length of other parallel side of Trapezium is 29 cm .

Answer 2

Answer:

Given :-

• The area of a trapezium of height is 24.2 cm and is 605 cm².
• One of the parallel sides is 21 cm.

To Find :-

• What is the other side of a trapezium.

Formula Used :-

$\clubsuit$ Area Of Trapezium Formula :

$\footnotesize \bigstar \: \: \sf\boxed{\bold{\pink{Area_{(Trapezium)} =\: \dfrac{1}{2} \times (Sum\: of\: Parallel\: Side) \times Height}}}\: \: \: \bigstar$

Solution :-

Let,

$\mapsto \bf Other\: Side_{(Trapezium)} =\: b\: cm$

Given :

• Area of Trapezium = 605 cm²
• One Parallel Side of Trapezium = 21 cm
• Height of Trapezium = 24.2 cm

According to the question by using the formula we get,

$\footnotesize \implies \sf\bold{\blue{Area_{(Trapezium)} =\: \dfrac{1}{2} \times (Sum\: of\: Parallel\: Side) \times Height}}$

$\implies \bf Area_{(Trapezium)} =\: \dfrac{1}{2} \times (a + b) \times h$

$\implies \sf 605 =\: \dfrac{1}{2} \times (21 + b) \times 24.2$

$\implies \sf 605 \times \dfrac{2}{1} =\: (21 + b) \times 24.1$

$\implies \sf \dfrac{605 \times 2}{1} =\: (21 + b) \times 24.1$

$\implies \sf \dfrac{1210}{1} =\: (21 + b) \times 24.1$

$\implies \sf 1210 =\: (21 + b) \times 24.2$

$\implies \sf 1210 \times \dfrac{1}{24.2} =\: 21 + b$

$\implies \sf \dfrac{1210 \times 1}{24.2} =\: 21 + b$

$\implies \sf \dfrac{1210}{24.2} =\: 21 + b$

$\implies \sf 50 =\: 21 + b$

$\implies \sf 50 - 21 =\: b$

$\implies \sf 29 =\: b$

$\implies \sf\bold{\green{b =\: 29}}$

Hence,

$\dag$ Other Parallel Side Of Trapezium :

$\dashrightarrow \sf Other\: Side_{(Trapezium)} =\: b\: cm$

$\dashrightarrow \sf\bold{\red{Other\: Side_{(Trapezium)} =\: 29\: cm}}$

$\small \sf\bold{\purple{\underline{\therefore\: The\: other\: parallel\: side\: of\: trapezium\: is\: 29\: cm\: .}}}$