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

Answer:

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}⟼ParallelSide=21cmandxcm

Using Formula :

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

AreaofTrapezium=

2

1

×(Sumofparallelsides)×h

Putting Values :

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

2

1

×(21+x)×24.2

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

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

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

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

242×

10

7018×

10

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

242

7018

\longmapsto\tt\bf{x=29\:cm}⟼x=29cm

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

Answer 2

Given:-

• Area of trapezium = 605 cm²
• Height, h = 24.2 cm
• One of the parallel side, a = 21 cm

To Find:-

• The other parallel side, b

Formula used:-

$\large{ \boxed{ \red{ \sf{Area \: \: \tiny{ (Trapezium) \large{ = \frac{1}{2} (a + b) \times h \large}}}}}}$

Where,

• a and b are parallel sides
• h is height

putting values,

$\large \sf \implies605 = \frac{1}{2} (21 + b) \times 24.2$

$\large \sf \implies605 = \frac{21}{2} + \frac{b}{2} \times \frac{242}{10}$

$\large \sf \implies605 \times \frac{10}{242} = 10.5+ \frac{b}{2}$

$\large \sf \implies25= 10.5+ \frac{b}{2}$

$\large \sf \implies25 - 10.5= \frac{b}{2}$

$\large \sf \implies14.5= \frac{b}{2}$

$\large \sf \implies14.5 \times 2= b$

$\large \sf \implies b= 29$

So, Other parallel side of trapezium= 29 cm