Answer :
To determine which calculation would not result in the correct area of the trapezoid given by the equation \( A = \frac{1}{2}(12)(3+7) \), let’s evaluate each option step-by-step:
### Step-by-Step Analysis:
1. Given Equation:
[tex]\[ A = \frac{1}{2} (12)(3 + 7) \][/tex]
2. Calculate the correct area:
[tex]\[ 3 + 7 = 10 \][/tex]
[tex]\[ A = \frac{1}{2} (12) (10) = \frac{1}{2} \times 120 = 60 \][/tex]
So, the correct area of the trapezoid is 60.
### Evaluate Each Option:
#### Option A: \(\frac{12(3+7)}{2}\)
First, we simplify inside the parentheses:
[tex]\[ 3 + 7 = 10 \][/tex]
Now substitute back into the equation:
[tex]\[ \frac{12 \times 10}{2} = \frac{120}{2} = 60 \][/tex]
Option A gives us the correct area of 60.
#### Option B: \(6(3+7)\)
First, we simplify inside the parentheses:
[tex]\[ 3 + 7 = 10 \][/tex]
Now substitute back into the equation:
[tex]\[ 6 \times 10 = 60 \][/tex]
Option B also gives us the correct area of 60.
#### Option C: \(0.5(12)(10)\)
First, we simplify inside the parentheses:
[tex]\[ 3 + 7 = 10 \][/tex]
Now substitute back into the equation:
[tex]\[ 0.5 \times 12 \times 10 = 0.5 \times 120 = 60 \][/tex]
Option C gives us the correct area of 60.
#### Option D: \(\frac{12}{2} \times \frac{10}{2}\)
Simplify each fraction separately:
[tex]\[ \frac{12}{2} = 6 \quad \text{and} \quad \frac{10}{2} = 5 \][/tex]
Now multiply the simplified fractions:
[tex]\[ 6 \times 5 = 30 \][/tex]
Option D gives us an incorrect area of 30.
### Conclusion:
The calculation that does not result in the correct area of the trapezoid is:
Option D: \(\frac{12}{2} \times \frac{10}{2}\).
So, the calculation [tex]\( \frac{12}{2} \times \frac{10}{2} \)[/tex] does not result in the correct area of the trapezoid. The correct calculations (Options A, B, and C) all give the area as 60.
### Step-by-Step Analysis:
1. Given Equation:
[tex]\[ A = \frac{1}{2} (12)(3 + 7) \][/tex]
2. Calculate the correct area:
[tex]\[ 3 + 7 = 10 \][/tex]
[tex]\[ A = \frac{1}{2} (12) (10) = \frac{1}{2} \times 120 = 60 \][/tex]
So, the correct area of the trapezoid is 60.
### Evaluate Each Option:
#### Option A: \(\frac{12(3+7)}{2}\)
First, we simplify inside the parentheses:
[tex]\[ 3 + 7 = 10 \][/tex]
Now substitute back into the equation:
[tex]\[ \frac{12 \times 10}{2} = \frac{120}{2} = 60 \][/tex]
Option A gives us the correct area of 60.
#### Option B: \(6(3+7)\)
First, we simplify inside the parentheses:
[tex]\[ 3 + 7 = 10 \][/tex]
Now substitute back into the equation:
[tex]\[ 6 \times 10 = 60 \][/tex]
Option B also gives us the correct area of 60.
#### Option C: \(0.5(12)(10)\)
First, we simplify inside the parentheses:
[tex]\[ 3 + 7 = 10 \][/tex]
Now substitute back into the equation:
[tex]\[ 0.5 \times 12 \times 10 = 0.5 \times 120 = 60 \][/tex]
Option C gives us the correct area of 60.
#### Option D: \(\frac{12}{2} \times \frac{10}{2}\)
Simplify each fraction separately:
[tex]\[ \frac{12}{2} = 6 \quad \text{and} \quad \frac{10}{2} = 5 \][/tex]
Now multiply the simplified fractions:
[tex]\[ 6 \times 5 = 30 \][/tex]
Option D gives us an incorrect area of 30.
### Conclusion:
The calculation that does not result in the correct area of the trapezoid is:
Option D: \(\frac{12}{2} \times \frac{10}{2}\).
So, the calculation [tex]\( \frac{12}{2} \times \frac{10}{2} \)[/tex] does not result in the correct area of the trapezoid. The correct calculations (Options A, B, and C) all give the area as 60.
