GED Mathematical Reasoning TestQuantitative Problem Solving with MeasurementMedium
A contractor is installing a new triangular window. The window has a base of 6 feet and a height of 8 feet. If glass costs $15 per square foot, what is the total cost of the glass for this window?
- A$180
- B$90
- C$720
- D$360
Show answer & explanationAnswer & explanation
Correct answer: D. $360
First, calculate the area of the triangular window using the formula A = (1/2) × base × height. A = (1/2) × 6 feet × 8 feet = (1/2) × 48 = 24 square feet. Then, multiply the area by the cost per square foot: 24 square feet × $15/square foot = $360.
Why the other options are wrong
- A. This would be the cost if the area was calculated as base × height (missing the 1/2 factor for a triangle).
- B. This would be the cost if the area was calculated as (base + height) or a significant underestimation.
- C. This would be the cost if the area was calculated as base × height and then multiplied by 2, or a significant overestimation.
Area of a Triangle
The area of a triangle is the amount of 2D space it covers, calculated as half of its base multiplied by its height.
- Formula: A = (1/2)bh
- Measured in square units.
- Base and height must be perpendicular.
Memory trick: Half the base, times the height, then cost for the window's light!