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Compare areas of shapes

Area is the amount of two-dimensional surface inside a shape, measured by the number of equal-sized square units that cover it without gaps or overlaps. Shapes can be compared by counting, organizing, decomposing, or recomposing unit squares, including rectangular arrays and multiplication; a shape with greater area need not have a greater perimeter or appear longer. This understanding excludes general formulas for arbitrary shapes, unit conversions, and fractional or decimal square units.

Detailed Explanation: Compare areas of shapes

Area tells how much space is inside a shape. We measure it by counting equal-sized square units that cover the shape with no gaps or overlaps.

To compare areas:

  1. Count the square units in each shape.
  2. Organize the squares into rows and columns.
  3. Multiply to find the total number of squares.
  4. Compare the totals. The shape with more square units has the greater area.

Example: Compare these two rectangular shapes.

  • Shape A has 4 rows with 3 squares in each row.
  • Shape B has 2 rows with 7 squares in each row.

Find each area:

Area of Shape A=4×3=12 square units\text{Area of Shape A}=4\times3=12\text{ square units} Area of Shape B=2×7=14 square units\text{Area of Shape B}=2\times7=14\text{ square units}

Now compare 1212 and 1414:

14>1214>12

So, Shape B has the greater area. It covers 14 square units, while Shape A covers 12 square units. A shape may look longer or narrower, so count or organize the square units instead of judging by appearance.

Learn by doing: Compare areas of shapes

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    Area of a Shape on a Grid - Largest Area, Either Shape

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