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The equation [tex]A=\frac{1}{2}(12)(3+7)[/tex] is used to find the area of a trapezoid. Which calculation would not result in the correct area?

A. [tex]\frac{12(3+7)}{2}[/tex]

B. [tex]6(3+7)[/tex]

C. [tex]0.5(12)(10)[/tex]

D. [tex]\frac{12}{2} \times \frac{10}{2}[/tex]

Sagot :

GinnyAnswer
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.
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