parallel sides of a Trapezium are 65 M and 40 M its non parallel sides are 39 M and 56 cm find the area of the trapezium
Answers
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....