Question

What is the perimeter of the perimeter of the polygon in the diagram?

Answer 1

Answer:

D

Step-by-step explanation:

Use the distance formula to find all of the sides.

Then add them together

Answer 2

Answer: $D.\ 4\sqrt{a^2+b^2}$

Step-by-step explanation:

From the given picture, it can be seen that the given polygon is dividede into four right triangles of same measurement.

Consider triangle in the first quadrant, then the base of triangle = |a-0|=a

Height of triangle = |b-0|=b

Let p be the side of the polygon which is also the hypotenuse of the given triangle.

Apply Pythagoras theorem in right triangle, we get

$p=\sqrt{a^2+b^2}$

Since all the triangles are congruent, then the perimeter of the polygon is given by :-

$4p=4\sqrt{a^2+b^2}$