Question

Find the perimeter of a polygon with vertices at A(0, 1), B(4, 4), C(7, 0), D(3, -3), E(-4, -4). Round your answer to the nearest hundredth.
Group of answer choices

40.55 units

25.00 units

32.00 units

28.47 units

Answer 1

It's interesting that areas from coordinates are much simpler than perimeters from coordinates.  It's almost like math is telling us area is more fundamental than length.

p = AB+BC+CD+DE+EA

We use the Pythagorean theorem, square root form, on all the sides.  We can skip a lot of the square roots because most of these are the hypotenuse of a 3/4/5 right triangle.

B-A=(4-0, 4-1)=(4,3) so length AB=5

C-B=(7-4,0-4)=(3,-4), so again  BC=5

D-C=(3-7, -3-0)=(-4,-3) so again CD=5

E-D=(-4-3, -4 - -3) = (-7, -1).  Ends our streak.  DE=√(7²+1²)=√50=5√2.

A-E=(0 - -4,1 - -4)=(4,5) so EA=√(4²+5²)=√41.

Three of five were 3/4/5.

p = 5+5+5+5√2+√41 = 15+5√2+√41

I hate to ruin a nice exact answer with an approximation.

p ≈ 28.474192049298324

Answer: 28.47, last choice