A lot consists of two nonoverlapping parts: a 100-foot by 80-foot rectangle and a triangle with 60-foot base and 40-foot perpendicular height. What is its total acreage, rounded to the nearest 0.01 acre?
Correct Answer
B) 0.21 acre
Rectangle area = 100 × 80 = 8,000 square feet. Triangle area = 60 × 40 ÷ 2 = 1,200 square feet. Total = 9,200 square feet. Dividing by 43,560 square feet per acre gives about 0.2112 acre, which rounds to 0.21 acre. The parts do not overlap and the triangle height is perpendicular. Common errors: not halving base × height for the triangle gives 0.24 acre; subtracting the triangle instead of adding it gives 0.16 acre; using 40,000 square feet per acre instead of 43,560 gives 0.23 acre.
Why This Is the Correct Answer
Option B is correct because the rectangle is 100 x 80 = 8,000 square feet and the triangle is 60 x 40 / 2 = 1,200 square feet, for a total of 9,200 square feet. Dividing by 43,560 square feet per acre gives about 0.2112 acre. Rounded to the nearest 0.01 acre, that is 0.21 acre.
Why the Other Options Are Wrong
Option A: 0.16 acre
Option A, 0.16 acre, subtracts the triangle as if it were cut out of the rectangle: (8,000 − 1,200) / 43,560 = 0.156, or 0.16 acre. The parts do not overlap, so the total is 9,200 / 43,560 = 0.21 acre.
Option C: 0.23 acre
Option C, 0.23 acre, results from using 40,000 square feet per acre: 9,200 / 40,000 = 0.23 acre. One acre is 43,560 square feet, so the correct result is 9,200 / 43,560 = 0.21 acre.
Option D: 0.24 acre
Option D, 0.24 acre, results from not halving base times height for the triangle: (8,000 + 2,400) / 43,560 = 0.24 acre. A triangle's area is 60 x 40 / 2 = 1,200 square feet, so the total is 9,200 square feet, or 0.21 acre.
Half the triangle, 43,560 per acre
Triangles take half of base times height, and acres come from dividing square feet by 43,560.
How to use: Use this checklist on any composite-lot acreage problem before choosing an answer.
Exam Tip
Compute each shape separately, add them, and only then convert to acres; check that you halved the triangle and used 43,560.
Common Mistakes to Avoid
- -Forgetting to halve base times height for the triangle
- -Using 40,000 square feet per acre instead of 43,560
- -Subtracting a nonoverlapping portion instead of adding it
Concept Deep Dive
Analysis
This question tests area calculation for a composite lot and conversion to acres. The rectangle and triangle are computed separately, added, and then divided by 43,560 square feet per acre. Each distractor reflects a specific common error such as forgetting to halve the triangle or using the wrong acre conversion.
Background Knowledge
Irregular lots are often measured by dividing them into simple shapes such as rectangles and triangles, calculating each area, and adding them. A rectangle's area is length times width, and a triangle's area is one-half base times perpendicular height. One acre equals 43,560 square feet.
Real-World Application
An appraiser receives a plat for an irregular lot shaped like a rectangle with a triangular extension. The appraiser calculates each portion, totals the square footage and converts it to acres to compare with the tax record.
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