ASVAB · Applied Geometry

A rectangular room measures 12 feet by 15 feet. Carpet costs $4 per square foot. How much will it cost to carpet the entire room?

Correct answer

$720

  1. A $180
  2. B $540
  3. C $720
  4. D $54

Why this is the answer

Multi-step problem: first find the area, then multiply by the unit cost. Area = 12 × 15 = 180 square feet. Cost = 180 × $4 = $720. Common mistake: computing the perimeter (2 × 12 + 2 × 15 = 54 feet) instead of the area — but carpet covers the floor area, not just the perimeter. The perimeter would be relevant for baseboards or molding. Always identify whether the problem asks for: linear measurement (perimeter, length, distance) — uses regular units; area measurement (floor coverage, paint coverage, land area) — uses square units; volume measurement (water, air, soil) — uses cubic units. Real-world applications: flooring/carpet (area × cost per sq ft); paint (area × cost per sq ft, with coverage adjustments for second coats); concrete (volume × cost per cubic yard); gravel (volume × cost per ton). Step-by-step approach to multi-step problems: identify all required calculations, solve each in turn, combine.
Source: ASVAB AR — Multi-Step Cost Problems

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About this topic: Applied Geometry

Applied geometry on the ASVAB means perimeter, area and volume of everyday shapes — carpet for a room, fencing for a yard, water in a tank. The formulas are simple; the trap is choosing area when the question needs perimeter, or forgetting units. This is one of 9 Arithmetic Reasoning questions on applied geometry, each with a full explanation on a single study page.

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