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22 July, 07:24

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

+2
Answers (1)
  1. 22 July, 07:37
    0
    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
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