# The Area of a Rectangle

A rectangle is a quadrilateral in which all four angles are right angles and the opposite sides are equal in length.

Let be a rectangle having and . Let be the diagonal which divides the rectangle into two right triangles, and .

__Example__:

In exchange for a square plot of land, one of whose sides is m, a man wants to buy a rectangular plot m long which is of the same area as the square plot. Find the width of the rectangular plot.

__Solution__:

One side of the square plot m.

The area of the square plot square m.

The length of the rectangular plot m.

The length of the rectangular plot area of the square plot.

The length of the rectangular plot square m.

the width of the rectangular plot m

__Example__:

How many tiles cm square will be required to pave a footpath m wide going around the outside of a grassy plot m long and m wide.

__Solution__:

The width of the foot path m.

The outside dimensions of the plot are m and m.

Now,

The outside area of the plot square m.

The inside area of the plot square m.

The area of the foot path outside area inside area square m.

The area of one tile square m.

The number of tiles required tiles.