Depth · one concept from first principles · step 2 of 4
The field loses 3 m on each side across and 2 m at the top and bottom.
Subtract both borders, not just one.
7.EE.A.1Draw A DiagramThe top and bottom strips run the full width x and are 2 m wide; the side strips fit between them, y-4 long and 3 m wide.
Cutting the border into rectangles keeps every piece linear.
7.G.B.6Identify SubproblemsThe path splits into a top and a bottom strip, each by , and two side strips, each by , so its area is the sum of those four rectangles.
Cut this way, the four rectangles cover the path with no gap and no overlap, so their areas add up to the path's area.
The side strips fit between the top and bottom strips, so their length is the full height minus at the top and at the bottom.
Each rectangle's area is its length times its width, since it is that many rows of unit squares.
Two side strips of give groups of minus groups of , which is .
Use the field's width and length.
Distribute the 2 and combine the constants.
7.EE.A.1Convert To AlgebraCombine like terms.
x-terms with x-terms, y-terms with y-terms, numbers with numbers.
7.EE.A.1Convert To AlgebraBreak a frame-shaped region into simple strips and the algebra stays easy.
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