How to find the area of a rectangle
Formulas for the area of a rectangle
The area of a rectangle is the product of its base and its height. We can also express the area of a rectangle as the product of its length and its width.
An area is always given in units of ???\text{length}^2??? (“length squared”). In other words, if the dimensions (base and height, or length and width) of a rectangle are given in inches, the units for area will be ???\text{in}^2??? (also called square inches); if the dimensions are given in centimeters, the units for area will be ???\text{cm}^2??? (also called square centimeters).
When we given a dimension in units of feet, we sometimes use a single quotation mark instead of the word “feet” or the abbreviation ft. For example, we could express ???6??? feet as ???6'???. For a dimension in units of inches, we sometimes use a double quotation mark instead of the word inches or the abbreviation in. For example, we could express ???37??? inches as ???37''???.
How to calculate the area of rectangles in different contexts
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How to convert to common units to find the area of a rectangle
Example
Find the area of the rectangle.
We’ll use the formula ???A=bh???, where ???A??? is area, ???b??? is the base, and ???h??? is the height of the rectangle. Plugging in the dimensions of the rectangle we’ve been given, we get
???A=bh???
???A=(12)(7)???
???A=84\ \text{ft}^2???
Let’s do one with an additional step.
Example
A rectangular mirror measures ???24??? inches by ???4??? feet. What is the area of the mirror?
To find the area of the mirror, the units must be the same. You can convert inches to feet by remembering that there are ???12??? inches in ???1??? foot.
???\frac{24\text{ inches}}{12\text{ inches}}=2\text{ feet}???
Now we can use the fact that the mirror is a rectangle to multiply the length and width of the mirror.
???A=lw???
???A=(2)(4)???
???A=8\ \text{ft}^2???
We could have also found the area in square inches by converting ???4??? feet to inches.
???4\text{ feet}\cdot\frac{12\text{ inches}}{1\text{ foot}}=48\text{ inches}???
Then the area in square inches would be
???A=lw???
???A=(24)(48)???
???A=1,152\ \text{in}^2???