Area of a Rectangle

To find the area \(A\) of a rectangle, we multiply the length \(L\) by the width \(W\). We have:

\[ A = L \times W. \]

A square is a special rectangle where the edges have the same length. Thus, a square of side length \(L \) will have an area of

\[ A = L \times L = L^2. \]

The area of a rectangle with length \(l\) and breadth \(b\) is \(l\times b\). In a rectangle, the measures of opposite sides are always equal.

Calvin's desk at work measures \(7\) feet by \(6\) feet. What is the area (in feet\(^2\)) that his desk occupies?

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The length is \(7\) feet, while the breadth is \(6\) feet.

Therefore, the area of the desk is \(7\times 6=42~\text{ft}^2\). \(_\square\)

What is the side length of a square, which has the same area as a 4 by 9 rectangle?

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The area of the rectangle is \( 4 \times 9 = 36 \). So, the area of the square is also 36.

If the side length of the square is \( s \), then we have \( s^2 = 36 \), or that \( s = 6 \) (reject negative ).

The area of a square is equal to the perimeter of the square. What is its side length?

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Let the side length be \(L \). Then, we have \( L^2 = \text{ area } = \text{ perimeter } = 4 L \). Solving this, we get \( L (L-4) = 0 \), and so \( L = 4, 0 \). We reject the case of \( L = 0 \), to obtain \( L = 4 \).