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math part 1 formulas and problems
Terms in this set (11)
A square parcel of farmland measures 1,320 feet from north to south. In the center of the parcel is eight acres of swampland that is not tillable. If the property sells for $2,000 per acre of tillable land, what is the selling price?
/ First, multiply the property's boundaries to find its square footage (1,320 feet × 1,320 feet = 1,742,400 square feet). Convert it to acreage (1,742,400 square feet ÷ 43,560 square feet per acre = 40 acres), subtract the unusable portion (40 acres � 8 acres = 32 acres), and multiply by the price per acre (32 acres × $2,000 = $64,000).
A square parcel measures 1/8 of a mile by 1/8 of a mile. How many acres is this property?
One-eighth of a mile is equivalent to 660 feet (5,280 feet ÷ 8 = 660 feet). Multiply to find its square footage (660 feet × 660 feet = 435,600 square feet), and then divide to find the number of acres (435,600 square feet ÷ 43,560 square feet per acre = 10 acres
Brian purchases two parcels of land, one measuring one square mile and the other containing five acres. If he paid $2,000 an acre, what was his total purchase price?
One square mile equals 640 acres. Add those to find the total acreage (640 acres + 5 acres = 645 acres). Multiply the acreage by the price per acre to find the total price (645 × $2,000 = $1,290,000).
A corn field with a depth of 900 feet and a frontage of 484 feet is bisected by an access road, leaving two triangular lots. If the land sells for $2,000 per acre, how much is each lot worth?
Each lot is worth $10,000. One way to solve this problem is to find the area of one of the triangular lots. Use the triangle area formula, Area = 1/2 Base × Height (900 feet × 484 feet × 0.5 = 217,800 square feet). Convert this to acreage (217,800 square feet ÷ 43,560 square feet per acre = 5 acres), and then multiply by the cost per acre (5 acres × $2,000 = $10,000). Alternatively, you can use the rectangle area formula (Area = Length × Width) to find the area of the entire corn field (900 feet × 484 feet = 435,600 square feet), divide to convert the square footage to acreage (435,600 square feet ÷ 43,560 square feet per acre = 10 acres), multiply by the cost (10 acres × $2,000 = $20,000), and divide by 2 to find the cost of one of the lots ($20,000 ÷ 2 = $10,000).
Jamie's house is mostly rectangular, measuring 30 feet by 40 feet. There is an enclosed triangular foyer in front, measuring four feet across, four feet along the perpendicular side, and 5.7 feet along the diagonal side. In the back, there is a screened porch, which is 40 feet long and 5 feet deep. To the side, there is an attached garage, which measures 10 feet by 20 feet. What is the square footage of the living area?
Keep in mind that a house's square footage is based on its outside dimensions, but excludes garages and porches. So, you would only need to calculate the area of the main part of the house (30 feet x 40 feet = 1,200 square feet) and the odd triangular foyer (4 feet x 4 feet x � = 8 square feet). Add the two together to find the square footage is 1,208 square feet.
A metes and bounds description reads as follows: "Start at the intersection of Route 120 and Wells Lane. Proceed due south 1,815 feet, then due east 1,200 feet. Proceed due north 1,815 feet, then return west to point of beginning." How many acres is this property?
It may help to sketch the property being described; once you do, you will notice that it is rectangular, and you can simply use the Area = Length × Width formula. Multiply the length and width to find that it is 2,178,000 square feet (1,815 ft. × 1,200 ft. = 2,178,000 sq. ft.). Convert this amount to acreage by dividing by 43,560 (2,178,000 ÷ 43,560 = 50 acres).
From the point of beginning, a property's boundaries run 1,500' in a southerly direction, then due west for 1,800', then due north for 500', then back to the point of beginning. How many square feet does the parcel contain?
The parcel contains 1,800,000 square feet. Divide the parcel into a triangle with a base 1,800' long and a height of 1,000', and a rectangle that measures 1,800' × 500'. The area of the triangle is 900,000 square feet: 1,800 × 1,000 = 1,800,000 ÷ 2 = 900,000. The area of the rectangle is also 900,000 square feet: 1,800' × 500' = 900,000. Add the area of the triangle to the area of the rectangle to find the area of the whole parcel: 900,000 + 900,000 = 1,800,000 square feet.
A rural lot runs 500 feet east/west along its northern boundary, and 600 feet east/west along its southern boundary. Its eastern boundary runs 200 feet due north/south, while its western boundary runs 224 feet in a diagonal northeast/southwest direction. The cost of the land is $6 per square foot. What is the cost of this lot?
It's best to diagram this type of problem to solve it. Once you draw it, you would then break it down into a triangle at left and a rectangle at right. The rectangle at right is 500 feet in length and 200 feet in height (500 feet x 200 feet = 100,000 square feet). The triangle at left is 200 feet in height and 100 feet at its base (200 feet x 100 feet x 1/2 = 10,000 square feet); you can ignore the 224 foot diagonal side, which does not factor into your calculations. Add the two components together (100,000 square feet + 10,000 square feet = 110,000 square feet) and then multiply by the cost per square foot (110,000 square feet x $6 per square foot = $660,000) to find its price.
suppose a semi-truck's trailer is 40 feet long, 9 feet wide, and 7 feet high.
How many cubic yards of storage space does it contain?
Here's how to solve the problem. First, multiply the trailer's length, 40 feet, by its width, 9 feet, by its height, 7 feet. That tells you the trailer's volume is 2,520 cubic feet. Since a cubic yard is 27 cubic feet, divide 2,520 by 27 to make the conversion from cubic feet to cubic yards. There are 93.33 cubic yards of storage space in the truck's trailer.
A warehouse is listed at 60 feet long by 90 feet wide, with 15-foot ceilings. The building rents for five cents per cubic foot per month. What is the amount of the monthly rental payment?
First, calculate the building's volume (60 x 90 x 15 = 81,000 cubic feet). Multiply that by the monthly rent rate to find the amount of the monthly payment (81,000 x $0.05 = $4,050).
"A contractor is building a sidewalk that will be 100 feet long, 6 feet wide, and 6 inches deep. How many cubic yards of concrete will be needed to complete the sidewalk?"
first make sure that the units of measurement match up. Six inches is half a foot, or 0.5 feet. 100 feet times 6 feet times 0.5 feet equals 300 cubic feet of concrete. Divide 300 cubic feet by 27, the number of cubic feet in a cubic yard. You'll determine that the contractor will require 11.1 cubic yards of concrete to complete the sidewalk.
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