## How to Use the Area of a Rectangle Formula

- Identify what measurements you were given.
- Identify which measurement you were asked to find.
- Substitute the given measurements into the Area of a Rectangle Formula and simplify or solve the equation until you find the measurement you are looking for.

## Examples

Find the width of the rectangle.

Find the area of the rectangle.

*What measurements were you given?*

The diagram tells me that the width of the triangle is \(\blue 6 \, in\).

\[\blue w=6\]

The diagram also tells me that the diagonal of the rectangle is \(\blue 10 \, in\). The Area of a Rectangle Formula does not have a variable for the diagonal of the rectangle, but I can use the diagonal, the width and the Pythagorean Theorem to find the length of the rectangle.

\[6^2+l^2=10^2\]

\[36+l^2=100\]

\[l^2=64\]

\[\blue l=8\]

*Which measurement were you asked to find?*

The measurement I want to find is the area of the rectangle.

\[\blue A=A\]

*Do you have all the variables required for the Area of a Square Formula?*

Yes, in Steps 1 and 2, I defined all three variables:

\[\blue w=6\]

\[\blue l=8\]

\[\blue A=A\]

When I substitute these values into the Area of a Rectangle Formula, I get…

\[{\blue A}=({\blue 8})({\blue 6})\]

I can simplify the right hand side of the equation by multiplying \(\blue 8\) and \(\blue 6\).

\[{\blue A}={\blue 48}\]

The area of the rectangle is \(\blue 48 in^2\).

Find the length of the rectangle.