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.
