A lot is 50 m by 40 m. A house 32 m by 9 m is built on the lot. How much area is left over?

Question:

A lot is 50 m by 40 m. A house 32 m by 9 m is built on the lot. How much area is left over?

Rectangle: Area

In a general case, the area of a rectangle with dimensions {eq}x {/eq} and {eq}y {/eq} is calculated using the product {eq}A = xy {/eq}.

Assume that we are given two rectangles with dimensions {eq}x_1, y_1 {/eq} and {eq}x_2, y_2 {/eq} respectively with the latter having greater dimensions. If a smaller rectangle is placed inside of a greater rectangle, the area between the two rectangles is then calculated by {eq}A_2 - A_1 = x_2y_2 - x_1y_1 {/eq}.

Given two rectangles with dimensions:

{eq}x_1 = 9~m\\ y_1 = 32~m\\ x_2 = 50~m\\ y_2 = 40~m {/eq}

The area that is left over can be calculated by the difference of areas:

{eq}A_2 - A_1 = x_2y_2 - x_1y_1 = 50~m\cdot 40~m - 32~m\cdot 9~m = 1712~m^2 {/eq}

Hence, a total of {eq}\boxed{1712~\rm{m^2}} {/eq} are left over.