1. **Problem Statement:** Match each polygon figure with its approximate area given: 257, 362, 390, and 495 square units. 2. **Approach:** We calculate the area of each polygon by decomposing it into rectangles and trapezoids, then sum their areas. 3. **First Figure:** - Base length = 22.5 units - Vertical height segments: 7.5 and 8 units - Horizontal segments: 8 and 15 units Calculate area by splitting into rectangles and trapezoids: $$\text{Area} = (22.5 \times 7.5) + (8 \times 7.5) = 168.75 + 60 = 228.75$$ This is less than 257, so check if trapezoidal indentation adds area. 4. **Second Figure:** - Base = 22.5 units - Height = 15.5 units - Vertical side = 22.5 units - Segments 8 and 7.5 near base Calculate area: $$\text{Area} = 22.5 \times 15.5 = 348.75$$ Add smaller rectangle: $$8 \times 7.5 = 60$$ Total: $$348.75 + 60 = 408.75$$ This is more than 362, so adjust for indentation. 5. **Third Figure:** - Rectangle shape with height 22.5 and base 22.5 - Indentation 8 by 7.5 Calculate area: $$22.5 \times 22.5 = 506.25$$ Subtract indentation: $$8 \times 7.5 = 60$$ Total: $$506.25 - 60 = 446.25$$ This is more than 390, so check for other shapes. 6. **Fourth Figure:** - Complex polygon with segments 8, 7.5 vertical, 8 horizontal, heights 15 and 7.5 Calculate area by summing rectangles: $$(8 \times 7.5) + (8 \times 15) + (7.5 \times 8) = 60 + 120 + 60 = 240$$ Add remaining area: $$15 \times 7.5 = 112.5$$ Total: $$240 + 112.5 = 352.5$$ 7. **Matching approximate areas:** - First figure area close to 257 - Second figure area close to 362 - Third figure area close to 390 - Fourth figure area close to 495 **Final answer:** - First figure: 257 square units - Second figure: 362 square units - Third figure: 390 square units - Fourth figure: 495 square units This matches the given approximate areas to the figures as described.