Subjects geometry

Perimeter Figure 498196

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Perimeter Figure 498196


1. **State the problem:** We need to find the perimeter of the shaded figure on the grid. 2. **Understand the shape:** The figure covers cells from (0,1) to (1,3) vertically, forming a 1-unit wide column 3 units tall, plus an additional block at (1,4) to (2,4). 3. **Recall perimeter definition:** The perimeter is the total length of the outer edges of the figure. 4. **Calculate vertical edges:** - Left side runs from (0,1) to (0,4) covering 3 units vertically. - Right side has two parts: from (1,1) to (1,3) (2 units) plus the block at (2,4) adding 1 unit vertically. 5. **Calculate horizontal edges:** - Bottom edge from (0,1) to (1,1) is 1 unit. - Top edges: from (0,3) to (1,3) is 1 unit plus from (1,4) to (2,4) is 1 unit. 6. **Count internal edges that do not contribute to perimeter:** - The edge between (1,3) and (1,4) is internal and not counted. 7. **Sum all outer edges:** - Left vertical: 3 units - Right vertical: 2 + 1 = 3 units - Bottom horizontal: 1 unit - Top horizontal: 1 + 1 = 2 units 8. **Total perimeter:** $$3 + 3 + 1 + 2 = 9$$ units **Final answer:** The perimeter of the shaded figure is **9** units.