A rectangular garden measures 24 meters by 15 meters. A rectangular flower bed measuring 8 meters by 6 meters is...
GMAT Geometry & Trigonometry : (Geo_Trig) Questions
A rectangular garden measures \(24\) meters by \(15\) meters. A rectangular flower bed measuring \(8\) meters by \(6\) meters is placed entirely inside the garden. What is the area, in square meters, of the garden that is not covered by the flower bed?
1. TRANSLATE the problem information
- Given information:
- Garden dimensions: 24 meters by 15 meters
- Flower bed dimensions: 8 meters by 6 meters
- Flower bed is entirely inside the garden
- Need to find: area of garden NOT covered by flower bed
- What this tells us: We need total garden area minus the flower bed area
2. INFER the solution approach
- Strategy: Calculate each rectangular area separately, then subtract
- This makes sense because the uncovered area = total area - covered area
3. Calculate the total garden area
- Area of garden = length × width = \(24 \times 15\) = \(360\) square meters
4. Calculate the flower bed area
- Area of flower bed = length × width = \(8 \times 6\) = \(48\) square meters
5. SIMPLIFY to find the final answer
- Uncovered area = Garden area - Flower bed area
- Uncovered area = \(360 - 48\) = \(312\) square meters
Answer: 312
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students misinterpret 'area not covered by the flower bed' and think they need to add the two areas together instead of subtracting.
Their reasoning: 'The problem mentions both the garden and flower bed areas, so I should add them: \(360 + 48 = 408\).'
This leads to confusion since 408 likely wouldn't match any reasonable answer expectation, causing them to second-guess their approach.
Second Most Common Error:
Incomplete INFER reasoning: Students calculate only one of the areas (usually just the garden area of 360) and think that's the final answer.
Their reasoning: 'The question asks for the garden area, so \(24 \times 15 = 360\) must be the answer.'
This causes them to miss the subtraction step entirely and provide 360 as their final answer.
The Bottom Line:
The key challenge is understanding that 'not covered by' creates a subtraction situation, not an addition one. Students need to visualize that the flower bed takes up space within the garden, leaving less area than the total garden area.