area and perimeter?

Question

What would be the area and perimeter of the following 2 properties.
*Begin at stake 1, go right 180 ft to stake 2, turn right, go 120 ft, turn right and go 60 ft to stake 3, go straight 60 ft, turn left go 60 ft, turn left and go 60 ft to stake 4, turn right, go 60 ft, turn right ft to stake 5, go straight 120 ft, turn right and go 90 ft to stake 6, turn left, go 30 ft, turn right and go 90 ft to stake 7, turn right, go 90 ft, turn left and go 60 ft, returning to stake 1
*Begin at stake 1, go right 100 ft to stake 2, turrn right, go 50 ft, turn right and go 25 ft to stake 3, turn left, go 25 ft, turn left and go 75 ft to stake 4, turn right, go 100 ft, turn right go 100 ft to stake 5, go straight 75 ft to stake 6, turn right, go 75 ft, turn left and go 50 ft to stake 7, turnn right go 100 ft turn right and go 75 ft, returning to stake 1.

Answer 1

The best way to work this problem is to get some graph paper out of your desk and draw it. Divide the surface is familiar geometrical figures (rectanges, squares...) and keep a tally of the areas. The perimeter is just the linear distance of the boundaries.

On this one...you do the rest of the work!

Answer 2

The boundaries for this area are from flag to flag, not the path given.
1.
P = 180 + √(120^2 + 60^2) + 60 + 60√2 + √(120^2 + 90^2) + √(30^2 + 90^2) + √(90^2 + 60^2)
P = 180 + 60√(2^2 + 1) + 60 + 60√2 + 30√(4^2 + 3^2) + 30√(1 + 3^2) + 30√(3^2 + 2^2)
P = 240 + 60√5 + 60√2 + 30√25 + 30√10 + 30√13
P = 390 + 30(2√5 + 2√2 + √10 + √13)
P = 390 + 30(2√5 + 2√2 + √10 + √13)
P = 812.0517605 ft.

A = (180 - 60)(60) + 60*120 + (180 - 90)(120) + 60*120/2 + 60*60/2 + 120*90/2 + 30*90/2 + 90*60/2
A = 7,200 + 7,200 + 10,800 + 3,600 + 1,800 + 5,400 + 1,350 + 2,700
A = 40,050 sq. ft.

2.
P = 100 + √(50^2 + 25^2) + √(25^2 + 75^2) + √(100^2 + 100^2) + 75 + √(75^2 + 50^2) + √(100^2 + 75^2)
P = 175 + 25√(2^2 + 1) + 25√(1 + 3^2) + 100√2 + 25√(3^2 + 2^2) + 25√(4^2 + 3^2)
P = 175 + 25√5 + 25√10 + 100√2 + 25√13 + 25√25
P = 175 + 25(√5 + √10 + 4√2 + √13 + 5)
P = 666.5187791 ft.

A = 75*75 + 25*50 + 75*75 + 25*50/2 + 25*75/2 + 100*100/2 + 75*50/2 + 100*75/2
A = 24,687.5 sq ft.

Answer 3

If the problem is right, for the first case you only get the length(1080ft) the area does not close!
The second one is the same (850 ft).
I drew them with a program.

Answer 4

Do it on graph paper, having each square represent ten feet or something.

Answer 5

Umm,, could you repost that question as an equasion plz? :0