Free practice
Area calculations: square footage and acreage
Finish →Question 1 of 40
Which measurement describes the surface contained within a parcel's boundaries?
Reveal answer
Correct answer: Area
Area measures the surface inside the boundaries. Perimeter, frontage, and depth are linear measurements.
Question 2 of 40
How many square feet are in one acre?
Reveal answer
Correct answer: 43,560
One acre contains 43,560 square feet. This is the area conversion factor, not a linear measurement.
Question 3 of 40
A rectangular lot measures 75 feet by 160 feet. What is its area?
Reveal answer
Correct answer: 12,000 square feet
Rectangle area = length × width = 75 × 160 = 12,000 square feet.
Question 4 of 40
A square courtyard has sides of 45 feet. What is its area?
Reveal answer
Correct answer: 2,025 square feet
Square area = side × side = 45 × 45 = 2,025 square feet.
Question 5 of 40
A triangular parcel has a base of 180 feet and a perpendicular height of 120 feet. What is its area?
Reveal answer
Correct answer: 10,800 square feet
Multiply base by height: 180 × 120 = 21,600. Divide by two: 21,600 ÷ 2 = 10,800 square feet.
Question 6 of 40
A parcel contains 130,680 square feet. How many acres does it contain?
Reveal answer
Correct answer: 3 acres
Acres = square feet ÷ 43,560 = 130,680 ÷ 43,560 = 3 acres.
Question 7 of 40
A tract contains 2.5 acres. What is its area in square feet?
Reveal answer
Correct answer: 108,900 square feet
Square feet = 2.5 × 43,560. Two acres = 87,120 square feet; half an acre = 21,780 square feet. Their sum is 108,900 square feet.
Question 8 of 40
An assistant reports that a 90-foot by 140-foot rectangular lot contains 460 square feet because 2 × (90 + 140) = 460. What best explains the error?
Reveal answer
Correct answer: The assistant calculated perimeter; the area is 12,600 square feet.
The sum 90 + 140 = 230, doubled to 460, is perimeter in feet. Rectangle area is 90 × 140 = 12,600 square feet.
Question 9 of 40
Which expression converts an area stated in square feet into acres?
Reveal answer
Correct answer: Square feet ÷ 43,560
Divide square feet by 43,560 square feet per acre to determine acres.
Question 10 of 40
A rectangular parcel measures 60 yards by 150 feet. What is its area in square feet?
Reveal answer
Correct answer: 27,000 square feet
Convert 60 yards to feet: 60 × 3 = 180 feet. Then 180 × 150 = 27,000 square feet.
Question 11 of 40
An L-shaped parcel fits inside a 200-foot by 180-foot rectangle, with a 60-foot by 50-foot rectangular corner missing. What is the parcel's area?
Reveal answer
Correct answer: 33,000 square feet
Outer rectangle: 200 × 180 = 36,000 square feet. Missing corner: 60 × 50 = 3,000 square feet. Parcel: 36,000 − 3,000 = 33,000 square feet.
Question 12 of 40
A parcel consists of two nonoverlapping rectangles: one is 100 feet by 80 feet, and the other is 40 feet by 60 feet. What is the total area?
Reveal answer
Correct answer: 10,400 square feet
First area: 100 × 80 = 8,000. Second area: 40 × 60 = 2,400. Total: 8,000 + 2,400 = 10,400 square feet.
Question 13 of 40
A trapezoidal lot has parallel sides of 100 feet and 160 feet, separated by a perpendicular distance of 90 feet. What is its area?
Reveal answer
Correct answer: 11,700 square feet
Add parallel sides: 100 + 160 = 260 feet. Average: 260 ÷ 2 = 130 feet. Multiply by height: 130 × 90 = 11,700 square feet.
Question 14 of 40
A triangle has a 150-foot base, an 80-foot perpendicular height, and a 100-foot sloping side. A trainee calculates 7,500 square feet using the sloping side. What is the correct assessment?
Reveal answer
Correct answer: The area is 6,000 square feet because the height must be perpendicular to the selected base.
Use the height perpendicular to the 150-foot base: 150 × 80 = 12,000; 12,000 ÷ 2 = 6,000 square feet. The 100-foot sloping side is not that height.
Question 15 of 40
Two rectangular lots have the same 400-foot perimeter. Lot X is 100 feet by 100 feet; Lot Y is 50 feet by 150 feet. Which comparison is correct?
Reveal answer
Correct answer: Lot X has 2,500 more square feet than Lot Y.
X: 100 × 100 = 10,000 square feet. Y: 50 × 150 = 7,500 square feet. Difference: 10,000 − 7,500 = 2,500 square feet in X's favor.
Question 16 of 40
Which statement correctly describes an acre?
Reveal answer
Correct answer: It is an area of 43,560 square feet without a required shape.
An acre is a unit of area equal to 43,560 square feet. It does not prescribe side lengths, perimeter, or shape.
Question 17 of 40
A rectangular tract measures one-half mile by one-quarter mile. How many acres does it contain?
Reveal answer
Correct answer: 80 acres
Convert lengths: 0.5 × 5,280 = 2,640 feet and 0.25 × 5,280 = 1,320 feet. Area = 2,640 × 1,320 = 3,484,800 square feet. Acres = 3,484,800 ÷ 43,560 = 80.
Question 18 of 40
A tract contains 1.25 square miles. How many acres does it contain?
Reveal answer
Correct answer: 800 acres
One square mile = 5,280 × 5,280 = 27,878,400 square feet; 27,878,400 ÷ 43,560 = 640 acres. Therefore 1.25 × 640 = 800 acres.
Question 19 of 40
A lot contains 900 square yards. How many square feet does it contain?
Reveal answer
Correct answer: 8,100 square feet
One square yard = 3 feet × 3 feet = 9 square feet. Therefore 900 × 9 = 8,100 square feet.
Question 20 of 40
A trainee converts 30 yards by 40 yards to 90 feet by 120 feet, multiplies to get 10,800 square feet, then multiplies by nine again. What correction is needed?
Reveal answer
Correct answer: Stop at 10,800 square feet; both dimensions were already converted.
30 × 3 = 90 feet; 40 × 3 = 120 feet; 90 × 120 = 10,800 square feet. Multiplying by nine again repeats a conversion already incorporated into both dimensions.
Question 21 of 40
An exam asks for included floor area in a 60-foot by 40-foot rectangular building footprint. It expressly excludes a 20-foot by 20-foot garage within that footprint. What area should be reported?
Reveal answer
Correct answer: 2,000 square feet
Footprint = 60 × 40 = 2,400 square feet. Excluded garage = 20 × 20 = 400 square feet. Included area = 2,400 − 400 = 2,000 square feet.
Question 22 of 40
Parcel A contains 0.6 acre. Parcel B contains 25,000 square feet. Which parcel is larger, and by how much?
Reveal answer
Correct answer: Parcel A by 1,136 square feet
A = 0.6 × 43,560 = 26,136 square feet. Difference = 26,136 − 25,000 = 1,136 square feet. A is larger.
Question 23 of 40
A 5-acre tract is divided into eight equal-area parcels with no area reserved for roads or common space. What is the area of each parcel in square feet?
Reveal answer
Correct answer: 27,225 square feet
Total area = 5 × 43,560 = 217,800 square feet. Each parcel = 217,800 ÷ 8 = 27,225 square feet.
Question 24 of 40
A square parcel's side length is doubled. How does its area change?
Reveal answer
Correct answer: It becomes four times as large.
If the original side is s, original area is s × s. The new area is (2s) × (2s) = 4s², four times the original area.
Question 25 of 40
A rectangular lot measures 165 feet by 264 feet. How many acres does it contain?
Reveal answer
Correct answer: 1 acre
Area = 165 × 264 = 43,560 square feet. Acres = 43,560 ÷ 43,560 = 1 acre.
Question 26 of 40
A triangular tract has a base of 660 feet and a perpendicular height of 396 feet. What is its acreage?
Reveal answer
Correct answer: 3 acres
Base × height = 660 × 396 = 261,360. Triangle area = 261,360 ÷ 2 = 130,680 square feet. Acres = 130,680 ÷ 43,560 = 3.
Question 27 of 40
An L-shaped tract is a 330-foot by 264-foot rectangle with a 66-foot by 132-foot corner removed. What is its acreage?
Reveal answer
Correct answer: 1.8 acres
Outer area = 330 × 264 = 87,120 square feet. Removed area = 66 × 132 = 8,712. Remaining area = 87,120 − 8,712 = 78,408. Acres = 78,408 ÷ 43,560 = 1.8.
Question 28 of 40
A land area is stated as 2 square miles. A student squares 2 × 5,280 to find its square footage. Which calculation correctly handles the given area?
Reveal answer
Correct answer: 2 × 5,280² = 55,756,800 square feet
One square mile is 5,280 × 5,280 = 27,878,400 square feet. Two square miles = 2 × 27,878,400 = 55,756,800 square feet. Squaring a two-mile side instead describes four square miles.
Question 29 of 40
A rectangle's length increases by 20%, and its width decreases by 20%. How does its area compare with the original?
Reveal answer
Correct answer: It is 4% smaller.
New length factor = 1 + 0.20 = 1.20. New width factor = 1 − 0.20 = 0.80. Area factor = 1.20 × 0.80 = 0.96. Reduction = 1 − 0.96 = 0.04 = 4%.
Question 30 of 40
For triangle area, what does the height paired with a selected base measure?
Reveal answer
Correct answer: The perpendicular distance from the opposite vertex to the line containing the base
The height is the perpendicular distance from the opposite vertex to the line of the selected base. A side length or an average of sides need not equal that height.
Question 31 of 40
A parcel contains 50,000 square feet. What is its acreage rounded to the nearest hundredth?
Reveal answer
Correct answer: 1.15 acres
50,000 ÷ 43,560 = 1.147842… acres. The thousandths digit is 7, so round the hundredths digit up: 1.15 acres.
Question 32 of 40
A 3-acre tract includes a 30-foot-wide rectangular strip running its full 290.4-foot length. If the entire strip is excluded from the requested area, how many acres remain?
Reveal answer
Correct answer: 2.8 acres
Strip area = 30 × 290.4 = 8,712 square feet. Strip acreage = 8,712 ÷ 43,560 = 0.2 acre. Remaining acreage = 3 − 0.2 = 2.8 acres.
Question 33 of 40
Which pair consists entirely of units used to report land area?
Reveal answer
Correct answer: Square feet and acres
Square feet and acres both measure area. Feet, yards, and miles without a square designation measure length.
Question 34 of 40
Which formula gives the area of a trapezoid when its two parallel sides and perpendicular height are known?
Reveal answer
Correct answer: Average the two parallel sides, then multiply by the perpendicular height.
Trapezoid area = (parallel side one + parallel side two) ÷ 2 × perpendicular height. This uses the average of the parallel side lengths.
Question 35 of 40
A rectangular parcel contains 0.75 acre and is 165 feet wide. What is its length?
Reveal answer
Correct answer: 198 feet
Convert area: 0.75 × 43,560 = 32,670 square feet. Since area = length × width, length = 32,670 ÷ 165 = 198 feet.
Question 36 of 40
A parcel consists of a 200-foot by 150-foot rectangle and a nonoverlapping triangular extension with a 200-foot base and a 60-foot perpendicular height. What is its acreage, rounded to the nearest hundredth?
Reveal answer
Correct answer: 0.83 acre
Rectangle = 200 × 150 = 30,000 square feet. Triangle = 200 × 60 ÷ 2 = 12,000 ÷ 2 = 6,000. Total = 30,000 + 6,000 = 36,000. Acres = 36,000 ÷ 43,560 = 0.826446…; rounded = 0.83 acre.
Question 37 of 40
A trapezoidal tract has parallel boundaries of 300 feet and 426 feet, with a perpendicular separation of 240 feet. How many acres does it contain?
Reveal answer
Correct answer: 2 acres
Sum of parallel sides = 300 + 426 = 726. Average = 726 ÷ 2 = 363 feet. Area = 363 × 240 = 87,120 square feet. Acres = 87,120 ÷ 43,560 = 2.
Question 38 of 40
Two nonoverlapping lots each contain 10,000 square feet. One analyst rounds each lot to 0.23 acre before adding; another adds the square footage before rounding. What combined acreage is correct to the nearest hundredth?
Reveal answer
Correct answer: 0.46 acre; adding square footage first preserves precision, even though both stated methods happen to agree here
Total = 10,000 + 10,000 = 20,000 square feet. Acres = 20,000 ÷ 43,560 = 0.459136…; rounded = 0.46. Each lot rounds to 0.23, whose sum also happens to be 0.46; this coincidence does not make early rounding preferable.
Question 39 of 40
Two rectangles are used to cover a parcel on a sketch. Their areas are 8,000 and 5,000 square feet, but they overlap by 1,000 square feet. What is the area covered by their union?
Reveal answer
Correct answer: 12,000 square feet
The area sum is 8,000 + 5,000 = 13,000 square feet, but it counts the overlap twice. Subtract one overlap: 13,000 − 1,000 = 12,000 square feet.
Question 40 of 40
A buyer needs at least 0.50 acre. A rectangular lot measures 100 feet by 217 feet. Which assessment correctly uses the actual area before rounding?
Reveal answer
Correct answer: It falls short by 80 square feet.
Required area = 0.50 × 43,560 = 21,780 square feet. Lot area = 100 × 217 = 21,700 square feet. Shortfall = 21,780 − 21,700 = 80 square feet. Rounded acreage does not satisfy an exact minimum.
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