1.7: Various Formulas, Part 1
Objectives:
1. To use formulas to
find the perimeter,
circumference, and
area of squares,
rectangles, triangles,
and circles
Assignment:
• 1.7 Various Formulas
Worksheet: 1-20
Objective 1
You will be able to use formulas to
find the perimeter, circumference,
and area of squares, rectangles,
triangles, and circles
Units vs. Square Units
The length of
something (a
segment, a room, a
board) is measured
in units: inches,
feet, centimeters,
meters, etc. It’s a
one-dimensional
measurement.
1
Length: 1 unit
Perimeter
The perimeter of a
polygon is the sum
of lengths of all the
segments that
make up the
polygon. It is
basically the
distance around
the shape.
5.35 cm
4.82 cm
3.72 cm
6.04 cm
4.30 cm
Perimeter = 5.35 + 4.82 +
6.04 + 4.30 +3.72 = 24.23 cm
Let’s Have Some π
The distance around a circle is its
circumference.
Circumference
Diameter
Units vs. Square Units
The area of
something (a
polygon, a floor, a
wall) is measured
in square units:
in2, ft2, cm2, m2,
etc. It’s a twodimensional
measurement.
1
1
Area: 1 square unit
Area
The area of a
plane figure is the
measure, in
square units, of
the region
enclosed by the
figure.
This is simply the number
of unit squares that can be
arranged to completely
cover the figure.
If two polygons are
congruent, what do you
suppose is true about
their areas?
Formula City
Exercise 1
Find the area and perimeter (or
circumference) of each figure.
Exercise 3
The Large Hadron
Collider is a circular
tunnel that spans a
27 km
circumference.
What is the
diameter of the
LHC ring?
Exercise 4
If the irrigated circular
field shown has an
area of 804.25 m2,
what is the length
of the rotating
sprinkler (the radius
of the circle)?
Exercise 5
Find the
area of
the figure
shown.
Exercise 6
Given any of the previous formulas, what
would it mean to solve for a particular
variable?
To solve for a variable in an equation or
formula means to isolate that variable on only
one side of the equation:
variable = everything else
Exercise 7
1. Solve 𝐶 = 2𝜋𝑟 for 𝑟. Then find the radius
of a circle with a circumference of 44 in.
4
𝜋𝑟 3
3
2. Solve 𝑉 =
for 𝑟. Then find the
radius of a sphere with a volume of 36
cm3.
Exercise 8
Sometimes the variable you are solving for is
part of an expression.
1. Solve 𝑃 = 2𝑙 + 2𝑤 for 𝑙. Then find the
length of the rectangle whose perimeter is
30 in. and whose width is 7 in.
2. Solve 𝐴 =
1
(𝑏1
2
+ 𝑏2 )ℎ for 𝑏1 .
Exercise 9
Write a formula for the area of a circle in
terms of its circumference. Then find the
area of a circle with a circumference of
12.5 cm.
1.7: Various Formulas, Part 1
Objectives:
1. To use formulas to
find the perimeter,
circumference, and
area of squares,
rectangles, triangles,
and circles
Assignment:
• 1.7 Various Formulas
Worksheet: 1-20