Question

The area of a trapezium shaped field is 448 Sqm. If the distance between two parallel sides is 14 m and one of the parallel side is 44 m, then the other parallel sides is *​

Answer 1

Given :-  

• Area of a Trapezium is 448 m²  
• Distance b/w parallel sides is 14 m  
• One of the parallel side is 44 m  

To Find :-  

• Other parallel side  

Solution :-  

~Here , We’re given the area of the trapezium, one of it’s parallel side and the distance b/w the parallel sides which is the height of the parallel sides . We can find the other parallel sides by putting the values in the formula of finding area of a trapezium  

_____________

→ As we know that ,  

$\sf Area\;of\;trapezium=\dfrac{1}{2} \times (a+b) \times h$

 

_____________

Where ,  

• a and b are the parallel sides  
• h is the height ( distance )  

_____________

→ By putting the values !  

$\sf \implies 448 = \dfrac{1}{2} \times ( a + 44 ) \times 14$

 

$\sf \implies 448 = ( a + 4 ) \times 7$

$\sf \implies ( a + 4 ) = \dfrac{448}{7}$

 

$\sf \implies ( a + 4 ) = 64$

$\sf \implies a = 64 - 4$

$\sf \implies a = 60$

Therefore ,  

Other parallel side is of 60 m  

_____________

Answer 2

⠀⠀⠀⠀⠀⠀${\rm{\purple{\underline{\underline{★Required \:Answer★}}}}}$

20 metres

⠀⠀⠀⠀⠀${\rm{\pink{\underline{\underline{★Solution★}}}}}$

${\rm{\red{\underline{\underline{Given : }}}}}$

• Area of trapezium shaped field is 448 m².
• Distance between the parallel sides is 14m.
• One of the parallel sides is of 44m.

${\rm{\blue{\underline{\underline{To \: Find: }}}}}$

• The measure of the other parallel side.

${\rm{\green{\underline{\underline{Formula \: Used: }}}}}$

$\rm Area \: of \: trapezium = \frac{sum \: of \: parallel \: sides \: }{2} \times height$

Let's denote the parallel sides by $d_{1}$ and $d_{2}$ where, $d_{1}$ is 44m

Now formula becomes :-

$\rm Area \: of \: trapezium = \frac{ d_{1} + d_{2} }{2} \times height$

Here, height is the distance between the parallels.

${\rm{\orange{\underline{\underline{Calculations : }}}}}$

Let the second parallel side ($d_{2}$) be x m.

$\rm Area \: of \: trapezium = \frac{ d_{1} + d_{2} }{2} \times height$

substituting the values,

$\longrightarrow\rm 448 = \frac{44 + x}{2} \times 14$

$\longrightarrow\rm 448 = \frac{44 + x}{ \cancel2} \times \cancel{14}$

$\longrightarrow\rm 448 = 44 + x \times 7$

$\longrightarrow\rm \frac{448}{7} = 44 + x$

$\longrightarrow\rm \frac{ \cancel{448}}{\cancel7} = 44 + x$

$\longrightarrow\rm 64 = 44 + x$

$\longrightarrow\rm x = 64 - 44$

$\longrightarrow\rm x = 20 \: metres$

Hence, the other parallel is of 20 metres.