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5-15.

Examine the rectangles formed with tiles below. For each figure, write its area as a product of the width and length and as a sum of its parts. Homework Help ✎

a.This rectangle has the following algebra tiles: The first row is composed of 1 x tile placed horizontally and 1 unit tile. The second and third row are the same as the first row. The fourth row is composed of 1 x squared tile and 1 x tile placed vertically to form a solid rectangle. .

  • Find the outside dimensions of the large rectangle.

    See dimensions below.

    This rectangle has the following algebra tiles: The first row is composed of 1 x tile placed horizontally and 1 unit tile. The second and third row are the same as the first row. The fourth row is composed of 1 x squared tile and 1 x tile placed vertically to form a solid rectangle. Also, looking at the left edge of the rectangle, the distance along the edge is 3 + x. Looking at the bottom edge, the distance is x + 1.

    As a product: multiply the dimensions of the large rectangle together.
    As a sum: add up the areas of all of the small rectangles.

    area as product (length)(width)
    area as sum

  1. This rectangle has the following algebra tiles: The first row is composed of 2 x tiles placed horizontally and 1 unit tile. The second row is the same as the first row. The third row is composed of 2 x squared tiles and 1 x tile placed vertically to form a solid rectangle.

  • Use the same method as part (a).

    This rectangle has the following algebra tiles: The first row is composed of 2 x tiles placed horizontally and 1 unit tile. The second row is the same as the first row. The third row is composed of 2 x squared tiles and 1 x tile placed vertically to form a solid rectangle. Also, looking at the left edge of the rectangle, the distance along the edge is 2 + x. Looking at the bottom edge, the distance is 2 x + 1.

    area as a product  (length)(width)
    product as a sum