To solve this problem, we need to determine the correct expression for calculating the area of a triangle. The formula for the area of a triangle is given by:
[tex]\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
Given:
- The base ([tex]\(\text{b}\)[/tex]) of the triangle is 21 inches.
- The height ([tex]\(\text{h}\)[/tex]) of the triangle is 12 inches.
First, we substitute the given values into the formula:
[tex]\[ \text{Area} = \frac{1}{2} \times 21 \times 12 \][/tex]
Now we calculate:
[tex]\[ \text{Area} = \frac{1}{2} \times 252 \][/tex]
[tex]\[ \text{Area} = 126 \text{ square inches} \][/tex]
Next, let's examine the given expressions to see which one matches our formula:
1. [tex]\((21 + 12) \times 2\)[/tex]
[tex]\[ = 33 \times 2 \][/tex]
[tex]\[ = 66 \][/tex]
This does not match our calculated area of 126, so this is incorrect.
2. [tex]\((21 \times 12) \div 2\)[/tex]
[tex]\[ = 252 \div 2 \][/tex]
[tex]\[ = 126 \][/tex]
This matches our calculated area of 126, so this is the correct expression.
3. [tex]\((21 + 12) \div 2\)[/tex]
[tex]\[ = 33 \div 2 \][/tex]
[tex]\[ = 16.5 \][/tex]
This does not match our calculated area of 126, so this is incorrect.
4. [tex]\((21 \times 12) \times 2\)[/tex]
[tex]\[ = 252 \times 2 \][/tex]
[tex]\[ = 504 \][/tex]
This does not match our calculated area of 126, so this is incorrect.
Therefore, the correct expression to calculate the area of the triangle is:
[tex]\[ (21 \times 12) \div 2 \][/tex]
