Answer:
58.38 sq. units
Step-by-step explanation:
Here, draw JM ⊥ KL.
This makes the quadrilateral IJML a rectangle because 3 of it's angles are right angle. This means, IJ = JM = 7 as opposite sides of rectangle are equal.
∴ KM = KL - LM = 20 - 7 = 13
Then, JML will be isosceles right triangle because one of the angles is 90° by construction, and the other one is 45°, which means the remaining angle is also 45°.
∴ JM = KM = 13.
Again, IJML is a rectangle, so, IL = JM = 13. So, height of the given trapezium is 13.
Let's find value of JK using pythagoras theorem:
JK² = MK² + MJ² = 13² + 13²
or, JK² = 2(13)²
or, JK = 13√2
Therefore,
Periemter of polygon IJKL = IJ + JK + KL +IL = 7 + 13√2 + 20 + 13
= 40 + 13√2
≈ 58.38 sq. units
