1. **Stating the problem:** We have a triangle ABC with sides BC = 10 ft, AB = 11 ft, and CA = 17 ft. We want to analyze or solve for properties of this triangle. 2. **Check if the triangle is valid:** The triangle inequality states that the sum of any two sides must be greater than the third side. Check: - $10 + 11 = 21 > 17$ (valid) - $11 + 17 = 28 > 10$ (valid) - $10 + 17 = 27 > 11$ (valid) All inequalities hold, so the triangle is valid. 3. **Find the area using Heron's formula:** Heron's formula for the area $A$ of a triangle with sides $a$, $b$, and $c$ is: $$ A = \sqrt{s(s-a)(s-b)(s-c)} $$ where $s$ is the semi-perimeter: $$ s = \frac{a+b+c}{2} $$ 4. **Calculate the semi-perimeter:** $$ s = \frac{10 + 11 + 17}{2} = \frac{38}{2} = 19 $$ 5. **Calculate the area:** $$ A = \sqrt{19(19-10)(19-11)(19-17)} = \sqrt{19 \times 9 \times 8 \times 2} $$ $$ = \sqrt{2736} $$ 6. **Simplify the square root:** $$ 2736 = 16 \times 171 $$ $$ A = \sqrt{16 \times 171} = 4\sqrt{171} \approx 4 \times 13.0767 = 52.31 $$ 7. **Final answer:** The area of triangle ABC is approximately $52.31$ square feet.