lesson
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Imagine you are ordering a custom glass cover for a tablet screen that measures 8.5 inches long and 5.2 inches wide.
How do we write a mathematical equation to represent the exact space this screen covers?
The Area Formula
The area of a flat shape is the total number of unit squares needed to completely cover its surface.
For any rectangle with length l and width w, multiplying the two dimensions counts all those square units at once, giving the formula A=l⋅w.
📊A clean interactive-style diagram illustrating the rectangle area formula. Shows a light-blue rectangle partitioned into rows and columns with length labeled 'l (length)' across the top and width labeled 'w (width)' along the left side. Inside the rectangle, faint grid lines show square units filling the space. Below the rectangle, large bold text displays the formula 'A = l · w' or 'A = b · h' with a colorful highlight badge explaining 'Area = Base × Height'. Use soft card container with rounded corners and high contrast labels.
A rational number is any number that can be written as a fraction ba, which includes whole numbers, decimals, and mixed numbers.
What happens when our measurements involve decimals instead of whole numbers?
Writing Equations with Decimals
Suppose a rectangular garden plot has a length of 4.5 meters and a width of 2.8 meters.
📊A visual diagram of a rectangular garden. The top edge is labeled '4.5 m' and the left edge is labeled '2.8 m'. Inside the rectangle, the area is labeled 'A'. Beside the rectangle, a step-by-step equation card shows: Step 1: Write formula 'A = l · w', Step 2: Substitute dimensions 'A = (4.5)(2.8)' or 'A = 4.5 · 2.8'. Highlight the variable A in blue and the numbers in coral. Clean modern card layout.
To write the equation for the area, replace l and w with the given values: A=(4.5)(2.8) or A=4.5⋅2.8
Decimals are straightforward — but what if the side lengths are given as fractions or mixed numbers?