Download Lecture Notes for Section 2.5 - Madison Area Technical College

Elementary Algebra Notes
Section 2.5
Page 1 of 5
Section 2.5: Formulas and Applications from Geometry
Big Idea: There are many formulas from geometry that can be used to solve real world problems.
Big Skill: You should be able to pick the correct geometric formula for a given geometry problem, and solve
the equation for the needed variable.
Perimeter: Perimeter is the distance around the outside of a two-dimensional shape.

The perimeter of a shape with straight sides is the sum of the lengths of its sides.

The perimeter of a circle is called its circumference.

The formula for the circumference of a circle is: C = 2r

Pi is an irrational numeric constant, and it is approximately given by:   3.14

Perimeter and circumference are measured in units of length, like feet or inches or yards or meters.
Practice:
1. What is the approximate radius of a circle that has a circumference of 22 centimeters?
2. If you have 2 feet of wood that is 2 inches wide, and you want to use it to make a square picture frame
with mitered corners, what is the size of the largest picture you can frame?
3. A farmer has 800 m of fencing to enclose a rectangular field. If the width of the field is 175 m, find the
length of the field.
4. Write a formula for the length of the side of an equilateral triangle in terms of the triangle’s perimeter.
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.
Elementary Algebra Notes
Section 2.5
Page 2 of 5
Area: Area is the measure of how many squares of a given dimension it takes to cover a geometric shape.

Area is measured in units of length2, like feet2 (i.e., square feet), or inches2 (i.e., square inches), or
2
yards (i.e., square yards), or meters2 (i.e., square meters).
Some geometric formulas for areas:
Rectangle
Arect  lw
Circle
Acirc  r 2
Triangle
Trapezoid
Atri 
Atrap 
1
bh
2
1
 B  b h
2
Sphere
Asphere  4 r 2
Box
Abox  2lw  2lh  2wh
Cylinder
Acyl  2 rh  2 r 2
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.
Elementary Algebra Notes
Section 2.5
Page 3 of 5
Practice:
5. The area of a triangle is 120 m2. If the height is 24 m, find the length of the base.
6. The Rogers Centre (formerly the SkyDome) in Toronto, Canada has a hemispherical roof with a
diameter of 630 feet. Find the area of the dome to the nearest square foot. Also, if a gallon of paint
covers 400 square feet, calculate how many gallons of paint are needed to paint the Rogers Centre dome.
7. A cylinder with a radius of 12 cm has an area of 500 cm2. Find its height.
8. Solve for the height of a cylinder in general in terms of its area and radius.
9. Solve for the height of a trapezoid in terms of its area and base lengths.
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.
Elementary Algebra Notes
Section 2.5
Page 4 of 5
Volume: Volume is the measure of how many cubes of a given dimension it takes to fill a geometric shape.

Volume is measured in units of length3, like feet3 (i.e., cubic feet), or inches3 (i.e., cubic inches), or
3
yards (i.e., cubic yards), or meters3 (i.e., cubic meters).
Some geometric formulas for volumes:
Box
Vbox  lwh
Cylinder
Vcyl  r 2 h
Sphere
4
Vsphere  r 3
3
Pyramid
1
Bh
3
B is the base area.
The base can be any
shape (not just a
square or rectangle)!
V pyr 
Cone
Vcone 
1
1
Bh  r 2 h
3
3
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.
Elementary Algebra Notes
Section 2.5
Page 5 of 5
Practice:
10. A dump truck has a rectangular box that is 3 yards wide by 5 yards long. What must be the height of the
box if it needs to contain a volume of 30 cubic yards?
11. If a can has a radius of 3.0 in., what must its height be if it is to hold a volume of 36 in.3?
12. If a pyramid has a volume of 225,000 ft.3 and a square base 200 ft. on a side, what is its height?
Angle facts:

The sum of the interior angles of a triangle is 180.

The sum of the interior angles of a rectangle is 360.

Angles that are on opposite sides of intersecting lines are equal.

Two angles that make a straight line are called supplementary, and add up to 180.

Two angles that make a right angle are called complementary, and add up to 90.
Practice:
13. If two supplementary angles are expressed as 6x + 29 and x + 11, what must x be?
14. If one angle of a triangle is double the smallest angle, and the other angle is triple the smallest angle,
what are the angles of the triangle?
Algebra is:
the study of how to perform multi-step arithmetic calculations more efficiently,
and the study of how to find the correct number to put into a multi-step calculation to get a desired answer.