To determine the area of a right triangle, we use the following formula:
[tex]\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]
In a right triangle, the two legs of the triangle serve as the base and the height. For this particular problem, the lengths of the legs are given as 7 mm and 13 mm.
1. Identify the base and the height of the triangle:
- Base ([tex]\( b \)[/tex]) = 7 mm
- Height ([tex]\( h \)[/tex]) = 13 mm
2. Substitute these values into the area formula:
[tex]\[ \text{Area} = \frac{1}{2} \times 7 \times 13 \][/tex]
3. Calculate the multiplication inside the formula:
[tex]\[ 7 \times 13 = 91 \][/tex]
4. Continue with the multiplication by [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[ \text{Area} = \frac{1}{2} \times 91 \][/tex]
5. Perform the final multiplication:
[tex]\[ \frac{1}{2} \times 91 = 45.5 \][/tex]
Therefore, the area of the right triangle whose leg lengths are 7 mm and 13 mm is:
[tex]\[ \boxed{45.5 \text{ mm}^2} \][/tex]
