### Home > CCA > Chapter 3 > Lesson 3.2.2 > Problem3-49

3-49.

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

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

$\left. \begin{array} { | c | c | c | } \hline x & { x } \\ \hline x & { x } \\ \hline x & { x } \\ \hline x ^ { 2 } & { x ^ { 2 } } & { x } & { x } & { x } \\ \hline \end{array} \right.$

height = x + 2 base = 2x + 4

To find the area as a product, area = base × height.

area = (2x + 4)(x + 2)

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

x + x + 1 + 1 + 1 + 1 + x + x + 1 + 1 + 1 + 1 + x² + x² + x + x + x + x = 2x² + 8x + 8

Area as a product = (2x + 4)(x + 2)
Area as a sum = 2x² + 8x + 8