SOLUTION: Pentagon ABCDE with vertices A(-6,2) B(-4,7) C(0,4) D(0,0) E(-4,-4) find the perimeter

Algebra ->  Triangles -> SOLUTION: Pentagon ABCDE with vertices A(-6,2) B(-4,7) C(0,4) D(0,0) E(-4,-4) find the perimeter       Log On


   

Question 913531: Pentagon ABCDE with vertices A(-6,2) B(-4,7) C(0,4) D(0,0) E(-4,-4)
find the perimeter
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You need to know the side lengths AB, BC, CD, DE, AE

To find the side length of say AB, you find the distance from A to B. So you'll use the distance formula. I'll show you how to find the distance from A to B

Solved by pluggable solver: Distance Formula


The first point is (x1,y1). The second point is (x2,y2)


Since the first point is (-6, 2), we can say (x1, y1) = (-6, 2)
So x%5B1%5D+=+-6, y%5B1%5D+=+2


Since the second point is (-4, 7), we can also say (x2, y2) = (-4, 7)
So x%5B2%5D+=+-4, y%5B2%5D+=+7


Put this all together to get: x%5B1%5D+=+-6, y%5B1%5D+=+2, x%5B2%5D+=+-4, and y%5B2%5D+=+7

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Now use the distance formula to find the distance between the two points (-6, 2) and (-4, 7)



d+=+sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2+%2B+%28y%5B1%5D+-+y%5B2%5D%29%5E2%29


d+=+sqrt%28%28-6+-+%28-4%29%29%5E2+%2B+%282+-+7%29%5E2%29 Plug in x%5B1%5D+=+-6, y%5B1%5D+=+2, x%5B2%5D+=+-4, and y%5B2%5D+=+7


d+=+sqrt%28%28-6+%2B+4%29%5E2+%2B+%282+-+7%29%5E2%29


d+=+sqrt%28%28-2%29%5E2+%2B+%28-5%29%5E2%29


d+=+sqrt%284+%2B+25%29


d+=+sqrt%2829%29


d+=+5.3851648071345

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Answer:


The distance between the two points (-6, 2) and (-4, 7) is exactly sqrt%2829%29 units


The approximate distance between the two points is about 5.3851648071345 units



So again,


Exact Distance: sqrt%2829%29 units


Approximate Distance: 5.3851648071345 units





So the distance from A to B is roughly 5.3851648071345 units.

That means AB is approximately 5.3851648071345 units long.

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You'd use the same formula and same basic steps to find the other side lengths. You can use this distance formula solver to help check your work.

Once you have all 5 side lengths, you add them all up to get the perimeter of the pentagon.

Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html

Thanks,

Jim