Question

Two parallel side of an isosceles trapezium are 6cmand 14cm respectively.if the length of each parallel side is 5cm, find the length of the parallel side

Answer 1

Answer:

see, dividing the trapezium into two triangle and one rectangle,

rectangle having one side =6 cm

triangle's sides are 5cm and 4cm

To find the third side or the perpendicular distance between both parallel lines,

Apply pythagoras' theorem.

height =√((5)² -(4)²)

          = 3 cm

so, area = (1/2)×(sum of parallel side)×(distance between them)

             = (1/2)×(6+ 14)×3

             = 30 cm²

Answer 2

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Answer:-
Let us consider a trapezium ABCD with 2 non parallel sides AB =CD = 5cm and 2 parallel sides BC = 6cm and AD = 14cm . Then when 2 non parallel sides are of equal length then parallel sides will be of formation such that when a bisector is drawn through one side it even bisects the other side .So , when we draw a perpendicular through B to AD or C to AD then we can get the perpendicular height 'h' = AL.

Now since AB and CD are equal AD will be equally distributed on both sides of BC so (14 - 6)/2 = 4cm = BL on both sides of BC .

Then by using Pythagoras theorerm,
=> AB² = AL² + BL²
=> 25 = h² + 16
=> h = 9cm
Then height of trapezium, h = 9cm


Step-by-step explanation:-
Now let us apply the formula for area of trapezium,
=> A = h(a+b)/2

=> A = 9(6+14)/2

=> A = 9*10

=> A = 90square cm

Hence , the area of the trapezium ABCD is 90square cm.









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