187
CH 33  RECTANGLES AND SQUARES
 Creating the Formulas
In Manhattan, Fifth Avenue (which runs north-south) meets 42nd
Street (which runs east-west) at a 90-degree angle, which is written
90.
A rectangle is a four-sided figure with all inside angles
90
90
equal to 90. This implies that the adjacent sides (sides
90
next to each other) are perpendicular and the opposite 90
sides are parallel. Notice that a square (where all four sides have the
same length) is also a four-sided figure with inside angles of 90 each.
Therefore, by definition, a square is a just a certain kind of rectangle.
We can conclude that every square is a rectangle, but certainly not
every rectangle is a square.
The distance around the rectangle (the sum of all four of its sides) is
called its perimeter. If l is the length of the rectangle and w is the
width, then the perimeter is P = l + l + w + w = 2l + 2w.
The area of a rectangle is a measure of the size of the region enclosed
within the rectangle. The formula for the area is A = lw. These two
formulas should follow logically from the chapter Intro to Geometry.
l
l
w
w
w
w
l
l
P = 2l + 2w
A = lw
(around the rectangle, like
fence around a yard)
(inside the rectangle, like
carpet inside a room)
Ch 33  Rectangles and Squares
188
As for the square, we can see that the perimeter, the distance around,
is simply four s’s added together, s + s + s + s, or 4s. The area of a
square, since it’s a special rectangle, is just the length times the width;
but the length and the width are both s, so the area is s  s, or s 2 .
s
s
s
P = 4s
A = s2
s
Homework
1.
The length of a rectangle is 17 ft. and its width is 13 ft. Find the
perimeter and the area of the rectangle.
2.
Find the perimeter and area of a square if each side of the square
is 25 in.
3.
If each side of a square is 23.7 yd, find its perimeter and area.
4.
Find the perimeter and area of a square each of whose sides is
2 3 mi.
5
5.
Find the perimeter and area of a square each of whose sides is
0.09 m.
6.
Find the perimeter and area of a rectangle whose length is
0.27 cm and whose width is 0.5 cm.
7.
Find the perimeter and area of a rectangle whose
length is 6 1 mm and whose width is 2 mm.
4
3
8.
Find the perimeter and area of a square each of
whose sides is 5 km.
8
Ch 33  Rectangles and Squares
189
9.
Find the perimeter and area of a square
each of whose sides is 3.07 m.
10.
Find the perimeter and area of a rectangle
whose length is 2.7 cm and whose width is
1.3 cm.
11.
Recall: A square
is just a special
kind of rectangle.
Find the perimeter and area of a rectangle whose length is 3 1
5
mm and whose width is 5 mm.
9
12.
Find the perimeter and area of a square each of whose sides is
1 2 ft.
7
13.
Find the perimeter and area of a rectangle whose length is 5 3 in
4
and whose width is 2 1 in .
8
14.
Find the perimeter and area of a square each of whose sides is
12.5 yd.
15.
Find the perimeter and area of a rectangle whose length is
12.3 mi. and whose width is 7.8 mi.
Solutions
Note: The symbol ft 2 means square feet, etc.
1.
P = 60 ft
A = 221 ft 2
2.
P = 100 in
A = 625 in 2
3.
P = 94.8 yd
A = 561.69 yd 2
4.
P = 10 2 mi
A = 6 19 mi 2
5
25
Ch 33  Rectangles and Squares
190
5.
P = 0.36 m
A = 0.0081 m 2
6.
P = 1.54 cm
A = 0.135 cm 2
7.
P = 13 5 mm
A = 4 1 mm 2
8.
P = 2 1 km
A = 25 km 2
64
9.
P = 12.28 m
A = 9.4249 m 2
6
2
6
10. P = 8 cm
A = 3.51 cm 2
11. P = 7 23 mm
A = 1 7 mm 2
12. P = 5 1 ft
A = 1 32 ft 2
13. P = 15 3 in
A = 12 7 in 2
14. P = 50 yd
A = 156.25 yd 2
15. P = 40.2 mi
A = 95.94 mi 2
45
7
4
9
49
32
“Perhaps the most valuable result of all education is the
ability to make yourself do the thing you have to do, when
it ought to be done, whether you like it or not; it is the first
lesson that ought to be learned; and however early a
man's training begins, it is probably the last lesson that he
learns thoroughly.”
Thomas H. Huxley (1825 - 1895)
Ch 33  Rectangles and Squares