Question

the parallel sides of a trapezium are 65 m and 40m its non parallel sides are 39 and 56 m find the area of trapezium
need best answer other wise I can report your answer.​

Answer 1

Answer:

Step-by-step explanation:

Heya User,

--> That's an interesting case out of trapezium ...

--> However, a construction of altitudes would work just fine...

--> Suppose AB = 40m

                     BD = 39m

                     CD = 65m

                     AC = 56m

Let us assume, AE = k || CE = x ...

Pythagoras on ΔACE gives :->

     -> k² + x² = 56²    ---> ( i )

Further, AB = FE { since, AE, BF are ||s }

=> EF = 40m => DF = ( 65 - 40 ) - CE = 25 - x

However, BF = AE = k --> { ||gm }

--> Pythagoras on ΔBFD gives :->

--> k² + ( 25 - x )² = 39²  ---> (ii)

--> ( ii ) - ( i ) :->

                  -50x + 625 = 39² - 56² = -1615

            =>  50x = 2240 => x = 44.8 m

Putting this in ( i ) and solving for 'k' , we have :->

--> Height of trapezium = 33.6m

Hence, Area of Trapezium = 1/2 * [ 40 + 65 ] * k = 1/2 * 105 * 33.6 m²

And therefore, the req.d Area is 1764 m²....