A triangular lot has a base of 200 feet and a height of 150 feet. What is the area of the lot?
Correct Answer
D) 15,000 sq ft
Step 1: Area of a triangle = Base × Height ÷ 2 = 200 × 150 ÷ 2 = 15,000 square feet.
Why This Is the Correct Answer
Step 1: Area of a triangle = Base × Height ÷ 2 = 200 × 150 ÷ 2 = 15,000 square feet.
Why the Other Options Are Wrong
Option A: 30,000 sq ft
This comes from multiplying base by height without dividing by 2.
Option B: 60,000 sq ft
This comes from multiplying base by height and then doubling.
Option C: 350 sq ft
This comes from adding the base and height instead of multiplying.
Deep Analysis of This Real Estate Math Question
Triangle area calculations apply to irregularly shaped lots that can't be measured as simple rectangles. The formula (base × height ÷ 2) represents half the area of a rectangle because a triangle is essentially a rectangle cut diagonally, making this calculation essential for accurate lot size determination and property taxation.
Background Knowledge for Real Estate Math
Geometric area calculations became standardized in surveying during the development of the Public Land Survey System in the late 1700s. Triangular lot measurements are particularly important in urban planning where lots must fit irregular street patterns, hillside developments, or waterfront properties with natural boundaries.
Memory Technique
Remember triangles are 'half rectangles' - visualize folding a rectangle along its diagonal, and you get two identical triangles. The phrase 'Triangle = Take half' reinforces that you must divide the base × height calculation by 2.
Exam Tip for Real Estate Math
Look for the word 'triangular' in the question stem as your cue to use base × height ÷ 2. If you see an answer choice that equals base × height without dividing by 2, it's likely a trap answer designed to catch the most common mistake.
Real World Application in Real Estate Math
A waterfront lot with 300 feet of shoreline frontage extends 200 feet inland in a triangular shape due to neighboring property lines. Using the triangle formula (300 × 200 ÷ 2 = 30,000 sq ft), the surveyor can calculate the exact lot size for deed preparation and tax assessment purposes.
Related Topics & Key Terms
Key Terms:
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