find the perimetre of trapezium
Answers
Answer:
LEGENDS WILL SURELY LIKE THIS
Answer: 36 units
Refer to the attachment.
Given figure is trapezium hence there is not a particular formula for finding the perimeter cuz there are Non Isosceles trapeziums too.
According to the diagram, this is an Isosceles trapezium as its non parallel sides are equal.
Perimeter :- Some of all the sides that close up the figure (lines that act as boundary) excluding those sides which are inside the figure.
Here, Perimeter is given by:
⇒ Sum of the parallel sides + Sum of the non-parallel sides
We are given the measurement of the parallel sides and height of the trapezium but not the measurement of the non-parallel sides so let's find it.
Drop a perpendicular from the vertex C on the line segment AD at point F which will be equal in magnitude to BE i.e., 4 units.
After construction, we get a rectangular shaped figure BEFC. In a rectangle opposite sides are equal. Hence,
- BC = EF = 10 units ...(i)
Now, we don't know the measurement of AE,
So let's find it out,
⇒ AD = 16 [ given ]
⇒ AE + EF + FD = 16
because, AE = FD, Because it is an isosceles trapezium.
⇒ AE + EF + AE = 16
⇒ 2AE + 10 = 16 [ EF = 10 units, eq.(i) ]
⇒ 2AE = 6
⇒ AE = 3
Now that, we have AE = 3 & BE = 4 (given),
In ∆ABE by Pythagoras theorem,
⇒ AB² = AE² + BE²
⇒ AB² = (3)² + (4)²
⇒ AB² = 25
⇒ AB = 5 units [ AE = -5 , neglected as length can't be negative. ]
Also,
- AB = CD = 5 units ...(ii)
[ Isosceles trapezium ]
As discussed earlier, Perimeter is given by,
⇒ Sum of parallel sides + Sum of non parallel sides
⇒ BC + AD + AB + CD
⇒ 10 + 16 + 5 + 5 [ AB=CD=5units, See eq.(ii) ]
⇒ 26 + 10
⇒ 36 units
Hence, Perimeter of the given trapezium is 36 units.
