1. **Problem:** Calculate the length |BE| to 1 decimal place. 2. **Given:** From the diagram, segment EC = 10.67 m, EF = 5.4 m, FC = 9.2 m, and BC = 3.1 m. 3. **Step 1: Understand the shape and points involved.** - Points B, E, and C form part of the 3D polyline/triangular prism-like shape. - We want to find the length |BE|. 4. **Step 2: Use the triangle or 3D distance formula.** - Since E and C are connected, and B to C is known, we can use the Pythagorean theorem or 3D distance formula if coordinates are known. 5. **Step 3: Calculate |BE| using the triangle BEC.** - We know BC = 3.1 m and EC = 10.67 m. - Assuming B, E, and C form a right triangle at C, then: $$|BE| = \sqrt{|BC|^2 + |EC|^2} = \sqrt{3.1^2 + 10.67^2}$$ 6. **Step 4: Calculate the value:** $$|BE| = \sqrt{9.61 + 113.8489} = \sqrt{123.4589} \approx 11.11$$ 7. **Answer:** $$|BE| \approx 11.1 \text{ m (to 1 d.p.)}$$