A lot consists of a nonoverlapping 100 ft by 150 ft rectangle and a triangle with base 80 ft and perpendicular height 60 ft. What is the total area in square feet?
Correct Answer
C) 17,400 square feet
100 ft × 150 ft + (80 ft × 60 ft)/2 = 15,000 + 2,400 = 17,400 square feet. Common errors: subtracting the triangle as if it were cut out of the rectangle gives 12,600 square feet; not halving base × height for the triangle gives 19,800 square feet; reporting only the triangle gives 2,400 square feet.
Why This Is the Correct Answer
Option C is correct because the total area equals the rectangle plus the triangle. The rectangle is 100 ft x 150 ft = 15,000 square feet, and the triangle is (80 ft x 60 ft) / 2 = 2,400 square feet. Adding them gives 15,000 + 2,400 = 17,400 square feet.
Why the Other Options Are Wrong
Option A: 2,400 square feet
Option A, 2,400 square feet, reports only the triangle: 80 x 60 / 2 = 2,400. The rectangle's 15,000 square feet must be added, for a total of 17,400 square feet.
Option B: 12,600 square feet
Option B, 12,600 square feet, treats the triangle as a cutout from the rectangle: 15,000 − 2,400 = 12,600. The two parts do not overlap, so their areas are added: 15,000 + 2,400 = 17,400 square feet.
Option D: 19,800 square feet
Option D, 19,800 square feet, comes from not halving base x height for the triangle: 100 x 150 + 80 x 60 = 15,000 + 4,800 = 19,800. The triangle is 4,800 / 2 = 2,400, so the total is 17,400 square feet.
Triangle takes half
A triangle is half of the rectangle drawn around it, so halve base times height. Then add the pieces.
How to use: Use this reminder whenever a lot or building is split into rectangles and triangles.
Exam Tip
Compute each piece separately and write it down before adding. Distractors usually show one piece alone or a triangle that was not halved.
Common Mistakes to Avoid
- -Forgetting to halve the triangle's base times height
- -Subtracting a nonoverlapping piece instead of adding it
- -Leaving out one of the component shapes
Concept Deep Dive
Analysis
This question tests composite area calculation. Break the lot into nonoverlapping shapes, compute each area with the correct formula, and add them. The rectangle is length times width; the triangle is one half of base times height.
Background Knowledge
Irregular lots are often measured by dividing them into rectangles and triangles. A triangle's area is one half of base times perpendicular height. Land area is commonly stated in square feet or acres, with 1 acre equal to 43,560 square feet.
Real-World Application
An appraiser measures an irregular commercial lot from a plat that shows a rectangle with a triangular extension. She computes each area separately, adds them, and compares her total with the area on the plat.
More Property Description Questions
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The subject is a 10-year-old dwelling with improvement cost new of $640,000. A highly comparable 7-year-old dwelling recently sold for $580,000; at the sale date its site was worth $150,000 and its improvement cost new was $500,000. Market evidence shows depreciation accruing evenly with actual age. What is the depreciated value of the subject improvements?
Observed sale prices are $450,000, $475,000, $425,000, $500,000, $440,000. Calculate the range (maximum−minimum), to the nearest dollar.
Observed values are 100, 105, 110, 115, 120. Calculate the range (maximum−minimum).
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For an arithmetic schedule only, allocate historical cost $2,500,000 over 40 years with zero residual. After 8 years, what unindexed scheduled amount remains? This is not an estimate of current market value.
The sale-price range is $45,000 and the maximum is $385,000. Find the minimum price.
A property is purchased for $1,500,000 with a loan of $1,200,000. Using the purchase price as the value, what is the loan-to-value ratio, as a percentage to one decimal?
Improvement cost new is $1,800,000. Separately supported improvement depreciation deductions of $200,000, $150,000, $100,000 are expressly nonoverlapping and not already excluded from cost new. No site is included. What depreciated improvement amount results?
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