To find the area of a triangle, the formula is [tex]\(\frac{1}{2} \times \text{base} \times \text{height}\)[/tex].
Given:
- Base = 21 inches
- Height = 12 inches
Let's go through each given expression to determine the correct one:
1. [tex]\((21 \times 12) \times 2\)[/tex]
- This expression calculates [tex]\(21 \times 12 = 252\)[/tex], then multiplies by 2, resulting in [tex]\(252 \times 2 = 504\)[/tex]. This does not match the formula for the area of a triangle.
2. [tex]\((21 + 12) \times 2\)[/tex]
- This expression sums the base and height [tex]\(21 + 12 = 33\)[/tex], then multiplies by 2, resulting in [tex]\(33 \times 2 = 66\)[/tex]. This also does not match the formula for the area of a triangle.
3. [tex]\((21 + 12) \div 2\)[/tex]
- This expression sums the base and height [tex]\(21 + 12 = 33\)[/tex], then divides by 2, resulting in [tex]\(33 \div 2 = 16.5\)[/tex]. This does not match the formula for the area of a triangle either.
4. [tex]\((21 \times 12) \div 2\)[/tex]
- This expression calculates [tex]\(21 \times 12 = 252\)[/tex], then divides by 2, resulting in [tex]\(252 \div 2 = 126\)[/tex]. This matches the formula for the area of a triangle, [tex]\(\frac{1}{2} \times \text{base} \times \text{height}\)[/tex].
So, the expression that correctly shows how to calculate the area of a triangle is:
[tex]\[ (21 \times 12) \div 2 \][/tex]
Therefore, the correct option is:
[tex]\[
\boxed{(21 \times 12) \div 2}
\][/tex]
