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 $L = 4$.