1. The problem asks for the area of a right triangle with vertical side $2 \frac{7}{10}$ mm and horizontal side $2 \frac{1}{8}$ mm. 2. Convert the mixed numbers to improper fractions: - $2 \frac{7}{10} = \frac{27}{10}$ mm - $2 \frac{1}{8} = \frac{17}{8}$ mm 3. The area of a right triangle is given by $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$. 4. Substitute the values: $$\text{Area} = \frac{1}{2} \times \frac{27}{10} \times \frac{17}{8}$$ 5. Multiply the fractions: $$\text{Area} = \frac{1}{2} \times \frac{459}{80} = \frac{459}{160}$$ 6. Simplify the fraction if possible. Since 459 and 160 have no common factors other than 1, this fraction is already in simplest form. 7. Convert to mixed number: $$\frac{459}{160} = 2 \frac{139}{160}$$ Final answer: $2 \frac{139}{160}$ square millimetres.