Question

Find the perimeter of the given figure:

Answer 1

Hint: We will first prove that the opposite sides are parallel and of equal length and after that we have to find the perimeter of this given figure just by adding all the four sides of this quadrilateral.

Complete step-by-step answer:
First we will state the definition of perimeter.
Perimeter: The sum of all the sides of a polygon.
Let’s name the quadrilateral ABCD in clock wise direction from the top left point.
So,
AB = 6 cm (upper line)
BC = 5 cm
CD = ?
DA = ?
Let’s find CD and DA,
From the given figure we can see that AB and CD are parallel.
And we have drawn a perpendicular line from A on the line CD which is of length 4 cm ( let that point be E)
AED is a right angle triangle given AE = 4 cm and DE = 3 cm.
So, applying Pythagoras theorem which is $hypotenuse=\sqrt{bas{{e}^{2}}+heigh{{t}^{2}}}$ .
So, AD = $\sqrt{D{{E}^{2}}+A{{E}^{2}}}=\sqrt{{{3}^{2}}+{{4}^{2}}}=5$ cm.
Hence, AD = BC and AB and CD are parallel so the given figure is parallelogram having length of opposite side same.
So, CD = 6 cm and DA = 5 cm.
Now we have everything that we need to calculate perimeter.
Therefore, perimeter = 6+5+6+5 = 22 cm.

Note: The most important part in this question is how to prove that the given figure is parallelogram, one can make mistakes in this part if he doesn't know the properties of parallelogram and then he or she will face difficulty in proving this statement.