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QuestionCalculate the area in acres of two land parcels in section 4: SW quarter of NW quarter of SE quarter of NW quarter and W half of SW quarter. Total area of section 4 is 640 acres. Possible answers: 82.5, 40, 100, 60 acres.

Studdy Solution

STEP 1

Assumptions1. The total area of section4 is640 acres. . Each quarter of a section is half the size of the previous section.
3. Each half of a section is half the size of the section.

STEP 2

First, let's find the area of the Southwest quarter of the Northwest quarter of the Southeast quarter of the Northwest quarter of section4.We know that each quarter is half the size of the previous section. So, we can calculate the area of each quarter by dividing the area of the previous section by4.
AreaSW of NW of SE of NW of section 4=Areasection 444Area_{SW\,of\,NW\,of\,SE\,of\,NW\,of\,section\,4} = \frac{Area_{section\,4}}{4^4}

STEP 3

Now, plug in the given value for the area of section to calculate the area of the Southwest quarter of the Northwest quarter of the Southeast quarter of the Northwest quarter of section.
Area_{SW\,of\,NW\,of\,SE\,of\,NW\,of\,section\,} = \frac{640\,acres}{^}

STEP 4

Calculate the area of the Southwest quarter of the Northwest quarter of the Southeast quarter of the Northwest quarter of section4.
AreaSW of NW of SE of NW of section 4=640 acres44=10 acresArea_{SW\,of\,NW\,of\,SE\,of\,NW\,of\,section\,4} = \frac{640\,acres}{4^4} =10\,acres

STEP 5

Next, let's find the area of the West half of the Southwest quarter of section4.We know that each half is half the size of the section. So, we can calculate the area of the West half of the Southwest quarter by dividing the area of the Southwest quarter by2.First, we need to find the area of the Southwest quarter. We can do this by dividing the area of section4 by4.
AreaSW of section 4=Areasection 44Area_{SW\,of\,section\,4} = \frac{Area_{section\,4}}{4}

STEP 6

Now, plug in the given value for the area of section4 to calculate the area of the Southwest quarter of section4.
AreaSW of section 4=640 acres4Area_{SW\,of\,section\,4} = \frac{640\,acres}{4}

STEP 7

Calculate the area of the Southwest quarter of section4.
AreaSW of section 4=640 acres4=160 acresArea_{SW\,of\,section\,4} = \frac{640\,acres}{4} =160\,acres

STEP 8

Now, we can find the area of the West half of the Southwest quarter by dividing the area of the Southwest quarter by2.
AreaWest half of SW of section 4=AreaSW of section 42Area_{West\,half\,of\,SW\,of\,section\,4} = \frac{Area_{SW\,of\,section\,4}}{2}

STEP 9

Plug in the value for the area of the Southwest quarter to calculate the area of the West half of the Southwest quarter.
AreaWest half of SW of section 4=160 acres2Area_{West\,half\,of\,SW\,of\,section\,4} = \frac{160\,acres}{2}

STEP 10

Calculate the area of the West half of the Southwest quarter.
AreaWest half of SW of section 4=160 acres2=80 acresArea_{West\,half\,of\,SW\,of\,section\,4} = \frac{160\,acres}{2} =80\,acres

STEP 11

Finally, we can find the total area of the two parcels of land by adding the areas we calculated in steps4 and10.
Total area=AreaSW of NW of SE of NW of section 4+AreaWest half of SW of section 4Total\,area = Area_{SW\,of\,NW\,of\,SE\,of\,NW\,of\,section\,4} + Area_{West\,half\,of\,SW\,of\,section\,4}

STEP 12

Plug in the values for the areas of the two parcels of land to calculate the total area.
Total area=10 acres+80 acresTotal\,area =10\,acres +80\,acres

STEP 13

Calculate the total area of the two parcels of land.
Total area=10 acres+80 acres=90 acresTotal\,area =10\,acres +80\,acres =90\,acresThe total area of the two parcels of land is90 acres.

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