Post on 26-Mar-2015
transcript
“A Little More Than An Acre”?
Jim is buying a field from Rob…
Rob says the area of the field is…
“… a little more than an acre.”
Jim says to himself…
“…I don’t trust Rob!”
“How can I know the area for sure?”
102 steps this way…
102
86
Keep walking…
102
115
86
Keep walking…
102
115
8186
Keep walking…
102
115
8186
Now diagonally…
112
Finally, I measure my own steps to be about 2.2 feet each…
Was Rob
s t r e t c h i n g
the truth?
“… a little more than an acre.”
102
115
8186112
1(102 86 112) 150
2s
Use Heron’s formula, taking the top triangle first…
102
115
8186112
150(150 102)(150 112)(150 86)
150(48)(38)(64)
4184.55
A
Use Heron’s formula, taking the top triangle first…
102
115
8186112
1(112 81 115) 154
2s
Now the bottom triangle…
102
115
8186112
154(154 112)(154 115)(154 81)
154(42)(39)(73)
4291.20
A
Now the bottom triangle…
102
115
8186112
4184.54 4291.20
8475.74 square paces
The sum of the areas is…
102
115
8186112
2
2 2.2 feet8475.74 paces
1 pace
Now for some unit conversions. First, convert square paces to square feet…
102
115
8186112
22 1 mile
41022.60 ft5280 feet
Then square feet to square miles…
102
115
8186112
2 640 acres.00147 mi
1 sq mile
And, finally, square miles to acres…
102
115
8186112
0.94 acres
The area of the field is…
Rob isa Liar!
“… a little more than an acre.”