Question

A farmer has a section of a field that measures (4 x 10^3) feet by (5 x 10^5) feet planted with carrots. Another section is planted with corn measuring, (6 x 10^4) feet by (3 x 10^4) feet. How much larger is the area of the carrot section than the corn section? What is the area of the carrot section? What is the area of the corn section?

Answer 1

First we have to calculate the area of the carrot section.

Using the formula for rectangle's area, which is base multiplied by the height.

`4\cdot10^3\cdot5\cdot10^5=4\cdot5\cdot10^3\cdot10^5=20\cdot10^8=2\cdot10^9\text{ .}`

The area of the carrot section is 2x10^9 square feet.

Then, we are going to calculate the area of the corn section.

`6\cdot10^4\cdot3\cdot10^4=6\cdot3\cdot10^4\cdot10^4=18\cdot10^8=1.8\cdot10^9\text{ .}`

The area of the carrot section is 1.8x10^9 square feet.

Subtracting the area of the corn section from the area of the carrot section we get

`2\cdot10^9\text{ -}1.8\cdot10^9=(2-1.8)\cdot10^9=0.2\cdot10^9=(2)/(10)\cdot10^9=2\cdot10^8`

a. The area of carrot section is 2x10^8 square feet greater than the area of the corn section.

b. The area of the carrot section is 2x10^9 square feet.

c. The area of the corn section is 1.8x10^9 square feet.