To determine the correct expression for calculating the area of a triangle with a given base of 21 inches and a height of 12 inches, let's explore the different given expressions step-by-step.
### Step-by-Step Breakdown
#### Expression 1: [tex]\((21 \times 12) \div 2\)[/tex]
1. Multiply the base and the height: [tex]\(21 \times 12 = 252\)[/tex]
2. Divide the result by 2: [tex]\(252 \div 2 = 126\)[/tex]
The area calculated using [tex]\((21 \times 12) \div 2\)[/tex] is 126 square inches. This is consistent with the formula for the area of a triangle, which is [tex]\(\frac{1}{2} \times \text{base} \times \text{height}\)[/tex].
#### Expression 2: [tex]\((21 \times 12) \times 2\)[/tex]
1. Multiply the base and the height: [tex]\(21 \times 12 = 252\)[/tex]
2. Multiply the result by 2: [tex]\(252 \times 2 = 504\)[/tex]
The area calculated using [tex]\((21 \times 12) \times 2\)[/tex] is 504 square inches. This is incorrect as it does not follow the triangle area formula, and results in a much larger number than expected.
#### Expression 3: [tex]\((21 + 12) \div 2\)[/tex]
1. Add the base and the height: [tex]\(21 + 12 = 33\)[/tex]
2. Divide the result by 2: [tex]\(33 \div 2 = 16.5\)[/tex]
The area calculated using [tex]\((21 + 12) \div 2\)[/tex] is 16.5 square inches. This is incorrect because it mistakenly treats the problem as a simple arithmetic operation rather than following the appropriate formula for the area of a triangle.
### Conclusion
The correct expression to calculate the area of a triangle with a base of 21 inches and a height of 12 inches is [tex]\((21 \times 12) \div 2\)[/tex].
Thus, the answer is:
[tex]\[ (21 \times 12) \div 2 \][/tex]
