A Little More Than An Acre?. Jim is buying a field from Rob…

“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.”