Land Area Math Problems and Solutions - Length, Width, Perimeter, Radius

Calculating land area is extremely important for every landowner, buyer, and seller. In this article, we will look at various types of land area math problems and their solutions. Learn how to calculate land area using length, width, perimeter, radius, and diameter.

Problem 1: Calculating Rectangular Land Area

Problem: If a plot of land has a length of 240 feet and width of 100 feet, what is the land area?

Solution:

Given: Length = 240 feet, Width = 90 feet, Area = ?

Using the formula:

Area = Length × Width
     = 240 × 90
     = 21,600 square feet

We know that 435.60 square feet = 1 Shotangsha (Decimal)

In Shotangsha = 21600 ÷ 435.60 = 49.59 Shotangsha

Answer: The land area is 49.59 Shotangsha

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Problem 2: Land Area with Feet and Inches

Problem: A plot of land has length 54 feet 5 inches and width 39 feet 9 inches. What is the land area?

Solution:

Given: Length = 54 feet 5 inches, Width = 39 feet 9 inches, Land area = ?

Since there are inches along with feet, we need to convert inches to feet for easier calculation.

Length = 54 + 5÷12 = 54 + 0.42 = 54.42 feet
Width = 39 + 9÷12 = 39.75 feet

Using the formula:

Area = Length × Width
     = 54.42 × 39.75
     = 2163.20 square feet

We know that 435.60 square feet = 1 Shotangsha

In Shotangsha = 2163.20 ÷ 435.60 = 4.97 Shotangsha (approximately)
In Katha = 2163.20 ÷ 720 = 3 Katha (approximately)

Answer: The land area is 4.97 Shotangsha or 3 Katha.

Note: This type of land plot is popular in urban and suburban areas.

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Problem 3: Land Area in Haat Unit

Problem: If a plot of land has length 27 Haat and width 36 Haat, what is the land area?

Solution:

Given: Length = 27 Haat, Width = 36 Haat, Land area = Area = ?

Using the formula:

Area = Length × Width
     = 27 × 36
     = 972 square Haat

We know that 193.60 square Haat = 1 Shotangsha.

In Shotangsha = 972 ÷ 193.60 = 5.02 Shotangsha

Answer: The land area is 5.02 Shotangsha

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Problem 4: Land Area in Meters

Problem: If a plot of land has length 24 meters and width 28 meters, what is the land area?

Solution:

Given: Length = 24 meters, Width = 28 meters, Area = ?

Using the formula:

Area = Length × Width
     = 24 × 28
     = 672 square meters

We know that 40.47 square meters = 1 Shotangsha.

In Shotangsha = 672 ÷ 40.47 = 16.60 Shotangsha

Answer: The land area is 16.60 Shotangsha

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Problem 5: Finding Length from Shotangsha

Problem: If a plot of land has an area of 25 Shotangsha and width of 90 feet, what is the length?

Solution:

Given: Land area = 25 Shotangsha, Width = 90 feet, Length = ?

You cannot directly divide Shotangsha by feet. Since width is in feet, we need to convert Shotangsha to square feet.

25 Shotangsha = 25 × 435.60 = 10,890 square feet

Using the formula:

Length = Area ÷ Width
       = 10,890 ÷ 90
       = 121 feet

Answer: The land is 121 feet in length

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Problem 6: Finding Width from Shotangsha

Problem: If a plot of land has area 4.06 Shotangsha and length 70 feet 9 inches, what is the width?

Solution:

Given:

• Area = 4.06 Shotangsha
• Length = 70 feet 9 inches = 70.75 feet
• Width = ?

We know that 1 Shotangsha = 435.60 square feet

4.06 Shotangsha = 435.60 × 4.06 = 1768.536 square feet

Using the formula:

Width = Area ÷ Length
      = 1768.536 ÷ 70.75
      = 25 feet

Answer: The width is 25 feet

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Problem 7: Rectangular Land Area and Diagonal

Problem: A rectangular plot has length 120 feet 9 inches and width 97 feet 7 inches. What is the land area and diagonal distance?

Solution:

Given:

• Length = 130 feet 9 inches = 130.75 feet
• Width = 95 feet 7 inches = 95.58 feet
• Area = ?
• Diagonal = ?

Using the formula:

Area = Length × Width
     = 130.75 × 95.58
     = 12497.085 square feet

We know that 435.6 square feet = 1 Shotangsha

In Shotangsha = 12497.085 ÷ 435.60 = 28.69 Shotangsha

Calculating Diagonal:

Diagonal = √(Length² + Width²)
         = √(130.75² + 95.58²)
         = √(17,095.5625 + 9,135.5364)
         = √26,231.0989
         = 161.96 feet (approximately)

Answer: Land area is 28.69 Shotangsha, Diagonal is 161.96 feet (approximately)

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Problem 8: Square Plot Land Area

Problem: A square plot has sides of 95 feet 9 inches. What is the land area?

Solution:

Given: Side = 95 feet 9 inches = 95.75 feet, Area = ?

Using the formula:

Area = Side × Side
     = 95.75 × 95.75
     = 9,168.0625 square feet

We know that 435.6 square feet = 1 Shotangsha

In Shotangsha = 9,168.0625 ÷ 435.60 = 21.05 Shotangsha

Answer: The land area is 21.05 Shotangsha

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Problem 9: Land Area in Links with Diagonal

Problem: A plot of land has length 180 links and width 30 links. What is the land area and diagonal?

Solution:

Given:

• Length = 180 links
• Width = 30 links
• Area = ?
• Diagonal = ?

Using the formula:

Area = Length × Width
     = 180 × 30
     = 5400 square links

We know that 1000 square links = 1 Shotangsha

In Shotangsha = 5400 ÷ 1000 = 5.4 Shotangsha

Calculating Diagonal:

Diagonal = √(Length² + Width²)
         = √(180² + 30²)
         = √(32400 + 900)
         = √33300
         = 182.48 links (approximately)

Answer: Land area is 5.4 Shotangsha, Diagonal is 182.48 links (approximately)

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Problem 10: Finding Side Length from Shotangsha

Problem: If a square plot has area 47.8 Shotangsha, what is the length of each side?

Solution:

Given: Area = 47.8 Shotangsha, Side = ?

We know that 1 Shotangsha = 435.6 square feet

47.8 Shotangsha = 47.8 × 435.60 = 20,821.68 square feet

Using the formula:

Side = √Area
     = √20,821.68
     = 144.30 feet

Answer: Each side is 144 feet 3 inches (approximately)

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Important Conversion Formulas

Conclusion

Accurately calculating land area is extremely important for buying and selling land. By practicing the problems above, you can calculate land area in various units. For quick and easy calculations, use our Land Area Calculator.

Related Conversions

• Square Feet to Satak Conversion
• Square Feet to Katha Conversion
• Satak to Katha Conversion
• Land Area Calculation Formulas