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Solution. If the corner square is 1 unit on a side, the area of the rectangle is the number of squares of
that size that fit inside the rectangle. As the next figure shows, 21 such square units fit inside, in 3 rows
of 7. The width (w)is evidently 3 units, and the length (l) 7 units. The area is the product 3 × 7= 21
square units.
7
width = 3 3
length = 7
The example illustrates a general fact: the area of a rectangle is the product of the length and
the width. If A denotes the area, the formula is
A = l · w.
It is also clear that the perimeter of a rectangle is the sum of twice the length and twice the
width, since to travel all the way around the boundary of the rectangle, both the length and the width
must be traversed twice. If P denotes the perimeter, the formula is
P =2l +2w.
Example 36. In the figure below we have drawn an L-shaped polygon on a grid. Find the area and
perimeter of the polygon. Take the unit of area to be one of the large squares of the grid, and assume
these squares are 1 cm on a side.
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