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Home > AC > Chapter 5 > Lesson 5.1.1 > Problem 5-6

5-6.

Write the area of the rectangle below as a product and as a sum. Homework Help ✎

Obtain algebra tiles from your teacher. These algebra tiles form a rectangle. First row: 2 positive x tiles placed horizontally and 4 positive unit tiles. Second row: same as first row. Third row: 2 positive x squared tiles and 4 positive x tiles placed vertically.

Find the height and the base by finding the dimensions of each row and column.

These algebra tiles form a rectangle. First row: 2 positive x tiles placed horizontally and 4 positive unit tiles. Second row: same as first row. Third row: 2 positive x squared tiles and 4 positive x tiles placed vertically. The height is the distance from top to bottom of the rectangle. The base is the distance from left to right of the rectangle. 

These algebra tiles form a rectangle. First row: 2 positive x tiles placed horizontally and 4 positive unit tiles. Second row: same as first row. Third row: 2 positive x squared tiles and 4 positive x tiles placed vertically. Looking at the left edge of the rectangle, the distance is x + 2. Looking at the bottom edge of the rectangle, the distance is 2 x + 4.

To find the area as a product, .

To express the area as a sum, add up all of the tiles and simplify.