This is the equation for the area of a rectangle.
| \( W \) | This symbol represents the width of a rectangle, meaning how large it is horizontally. |
| \( A \) | This is the symbol for area, meaning how much space there is inside a two dimensional shape. It is measured in any unit of length (often meters) squared \(\htmlClass{udt-0000000004}{m} ^{2}\). |
| \( H \) | This symbol represents the height of a rectangle, meaning how large it is vertically. |
Consider that we are trying to find the amount of space in a shape with the area:
The symbol for area is \(A\). It represents how much space there is inside a two dimensional shape. It is measured in any unit of length (often meters) squared \(\htmlClass{udt-0000000004}{m} ^{2}\). Different shapes have different formulas for calculating their area. Understanding area is crucial for various practical applications, including land measurement, interior design, and architecture, where efficient space utilization is essential. These calculations allow for the assessment and comparison of spaces, contributing to efficient planning and resource allocation.
Let us now consider a rectangle divided up into boxes, each one unit (\( \htmlClass{udt-0000000001}{\text{units}} \)) in length and one unit (\( \htmlClass{udt-0000000001}{\text{units}} \)) in height. An illustration of this can be seen in the following figure:
Now, to get the area, we can simply count the number of squares. If we count them we find that there are 50, meaning the area is 50 \(\htmlClass{udt-0000000001}{\text{units}}^2\).
We can also realize that the height (\( \htmlClass{sdt-0000000110}{H} \)) of the rectangle is 5 \( \htmlClass{udt-0000000001}{\text{units}} \), as each side of the squares inside are 1 \( \htmlClass{udt-0000000001}{\text{units}} \). By the same logic, we see that the width of the rectangle is 10 \( \htmlClass{udt-0000000001}{\text{units}} \). We can notice that \(5 \cdot 10 = 50\), the same as our answer.
We can generalize this to any rectangle to get the formula:
\[ \htmlClass{sdt-0000000115}{A} = \htmlClass{sdt-0000000107}{W} \cdot \htmlClass{sdt-0000000110}{H} \]
as required.
Consider a rectangle with width 3\( \htmlClass{udt-0000000004}{m} \) and height 5\( \htmlClass{udt-0000000004}{m} \). What is it's area?
\(\htmlClass{sdt-0000000107}{W} = 3\htmlClass{udt-0000000004}{m}\)
\(\htmlClass{sdt-0000000110}{H} = 5\htmlClass{udt-0000000004}{m}\)
We can directly plug them in to get:
\[ \htmlClass{sdt-0000000115}{A} = 5 \cdot 3 = 15 \]
The answer is therefore \(15\htmlClass{udt-0000000004}{m}^2\)