GED Mathematical Reasoning TestQuantitative Problem Solving with MeasurementHard
A worker needs to replace a square piece of glass in a window frame. The diagonal measurement of the square window is 30 inches. What is the approximate area of the glass needed, in square inches?
- A900 in²
- B450 in²
- C225 in²
- D600 in²
Show answer & explanationAnswer & explanation
Correct answer: B. 450 in²
For a square, the diagonal (d) relates to the side (s) by the Pythagorean theorem: s² + s² = d², or 2s² = d². This means s² = d²/2. Since the area of a square is s², the area can be directly calculated as d²/2.
Why the other options are wrong
- A. This is the result of 30², which is the area of a square with a side of 30, not diagonal.
- C. This is the result of (30/2)² or other incorrect calculations.
- D. This is an overestimation, possibly from incorrect formula application.
Area of a Square from Diagonal
The area of a square can be calculated directly if only its diagonal length is known.
- Formula: Area = d²/2
- Derived from Pythagorean theorem: s² + s² = d² => 2s² = d² => s² = d²/2
- Where 'd' is the length of the diagonal
Memory trick: Diagonal Squared, Then Halved, for Square Area