2-dimensional shapes: perimeter, circumference, and area
1
The distance around a polygon: Perimeter
The perimeter of a polygon is the distance around its boundary.
• This will be the sum of the lengths of all of its sides.
• The units will be the same as the units for the lengths of the sides.
1. Find the perimeter of each polygon. (They are not drawn to exact scale.)
Include the units in your answer.
2m 1m
@
3m
a.
b.
w
20 in
c.
10 cm
40 in
d.
b
f.
l
h
e.
s
2. Fill in the blanks: a formula for the perimeter of a rectangle with length l
and width w is
.
3. Fill in the blanks: a formula for the perimeter of a rectangle with base b
and height h is
.
4. Fill in the blanks: a formula for the perimater of a square with side length
s is
.
1
2
The distance around a circle: circumference
'$
r
&%
Circumference of a circle of diameter d and radius r: C = 2πr
C = πd
'$
θ◦
r
&%
arc length of the arc intercepted by an angle measuring θ ◦ :
θ
s
=
(2πr )
|{z}
360
| {z }
| {z } circum f erence
arc length
f raction
1. Find the circumference. Include the units in your answer.
(a)
'$
4 ft.
&%
(b)
'$
6 mm
s
&%
2. Find the arc length intercepted by each angle. Include the units in your
answer.
(a)
'$
10 km
&%
(b)
'$
◦
30
1 mi.
&%
2
3
Area
Shape name
picture
Formula for area
l = length
w = width
A = area
A = lw
w
l
rectangle
b = base
h = height
A =area
A = bh
h
b
s
s = side length
A = area
A = s2
s
square (which is a special rectangle)
J
h J
J
b
triangle
|
h
b
H
@H
@HHH
@
H
b
A
h A
A
A
A
A
A
parallelogram
b = base
h = height
A = area
A = 12 bh
HH
h H
H
{z
}
b
A
b
h
B
trapezoid
A
A
b = base
h = height
A = area
A = bh
B = larger base
b = smaller base
h = height
A=
area
A=
3
circle
B+b
2
'$
r
&%
r = radius
A = area
A = πr2
h
1. Find the area of each shape below. Include the units in your answer.
Draw a picture/sequence of pictures to explain your answer:
• For rectangles, draw in grid marks so that we can count the number
of square units
• For all other shapes, break the shape into rectangles and right triangles. Either place two right triangles together to form a rectangle or
draw in the rectangle of which a single right triangle is half.
3in.
8 in.
a.
b.
A
3 cm
A
|
{z
}
5cm
@
40 mm
c
@
Q
@
@
20 mm
2km
Q
d.
Q
Q
Q
Q
6 km
8 ft.
2 ft.
e.
2 ft.
2. Find the area of each circle. Include the units in your answer.
'$
3m
2 cm
a. &% b.
4