Names of polygons

1. Names of Polygons
Name Sides Angles
Triangle 3 3
Quadrilateral 4 4
Pentagon 5 5
Hexagon 6 6
Heptagon 7 7
Octagon 8 8
Nonagon 9 9
Decagon 10 10
Types of triangles based on their angles
A RIGHT triangle has one 90
o
angle.
An OBTUSE triangle has one angle that is greater than 90
o
.
An ACUTE triangle has all three angles less than 90
o
.
Types of triangles based on their sides
An EQUILATERAL triangle has all three sides the same length.
An ISOSCELES triangle has two sides with the same length.
A SCALENE triangle has all three sides different lengths.

The sum of the interior angles of a triangle are equal to 180
o
. To find the
third angle of a triangle when the other two angles are known subtract the
number of degrees in the other two angles from 180
o
.
Example: How many degrees are in the third angle of a triange whose other
two angles are 40
o
and 65
o
? Answer: 180
o
- 40
o
-65
o
= 75
o


Finding the Fourth Angle of a Quadrilateral
The sum of the interior angles of a quadrilateral are equal to 360
o
. To
find the fourth angle of a quadrilateral when the other three angles
are known, subtract the number of degrees in the other three angles
from 360
o
.
Example: How many degrees are in the fourth angle of a quadrilateral
whose other three angles are 80
o
and 110
o
and 95
o
? Answer: 360
o
-
80
o
- 110
o
- 95
o
= 75
o

Two angles are complementary if the sum of their angles equals 90
o
.
If one angle is known, its complementary angle can be found by subtracting
the measure of its angle from 90
o
.
Example: What is the complementary angle of 43
o
?
Solution: 90
o
- 43
o
= 47
o

Two angles are complementary if the sum of their angles equals 90
o
.
If one angle is known, its complementary angle can be found by subtracting
the measure of its angle from 90
o
.

2. Example: What is the complementary angle of 43
o
?
Solution: 90
o
- 43
o
= 47
o

Two angles are supplementary if the sum of their angles equals 180
o
.
If one angle is known, its supplementary angle can be found by subtracting
the measure of its angle from 180
o
.
Example: What is the supplementary angle of 143
o
?
Solution: 180
o
- 143
o
= 37
o


Two angles are supplementary if the sum of their angles equals 180
o
.
If one angle is known, its supplementary angle can be found by subtracting
the measure of its angle from 180
o
.
Example: What is the supplementary angle of 143
o
?
Solution: 180
o
- 143
o
= 37
o

Definitions of Sin, Cosine and Tangent
A right triangle consists of one angle of 90
o
and two acute angles.
Each acute angle of a right triangle has the properties of sine, cosine
and tangent. The sine, cosine and tangent of an acute angle of a right
triangle are ratios of two of the three sides of the right triangle.
The sine of the angle is the ratio of the length of the side opposite the
angle divided by the length of the hypotenuse.
The cosine of the angle is the ratio of the length of the side adjacent
to the angle divided by the length of the hypotenuse.
The tangent of the angle is the ratio of the length of the side opposite
the angle divided by the length of side adjac ent to the angle.

Calculating the Area of a Square
How to find the area of a square:
The area of a square can be found by multiplying the base
times itself. This is similar to the area of a rectangle but the
base is the same length as the height.
If a square has a base of length 6 inches its area is 6*6=36
square inches

Calculating the Area of a Rectangle
How to find the area of a rectangle:
The area of a rectangle can be found by multiplying the base
times the height.
If a rectangle has a base of length 6 inches and a height of 4
inches, its area is 6*4=24 square inches

Calculating the Area of a Parallelogram

3. How to find the area of a parallelogram:
The area of a parallelogram can be found by multiplying the
base times the height.
If a parallelogram has a base of length 6 inches and a height of
4 inches, its area is 6*4=24 square inches

Calculating the Area of a Trapezoid
A trapezoid is a quadrilateral (has 4 sides) and has only one pair of sides parallel.
How to determine the area of a trapezoid:
Add the lengths of the 2 parallel sides
divide by 2 to get the average length of the parallel sides.
Multiply this by the height (distance between the parallel sides

Calculating the Area of a Triangle
How to find the area of a triangle:
The area of a triangle can be found by multiplying the base
times the one-half the height.
If a triangle has a base of length 6 inches and a height of 4
inches, its area is 6*2=12 square inches
Finding the Area of a Circle
How to find the area of a circle:
The area of a circle can be found by multiplying pi ( π = 3.14)
by the square of the radius
If a circle has a radius of 4, its area is 3.14*4*4=50.24
If you know the diameter, the radius is 1/2 as large.

Calculating the Perimeter of a Square
The perimeter of a square is the distance around the outside of the
square. A square has four sides of equal length. The formula for
finding the perimeter of a square is 4*(Length of a Side).

Calculating the Perimeter of a Rectangle
The perimeter of a rectangle is the distance around the outside of the
rectangle. A rectangle has four sides with opposite sides being
congruent. The formula for finding the perimeter is Side A + Side B +

4. Side A + Side B. This could also be stated as 2*Side A + 2*Side B or
2*(Side A + Side B)

Calculating the Perimeter of a Parallelogram
The perimeter of a parallelogram is the distance around the outside of
the parallelogram. A parallelogram has four sides with opposite sides
being congruent. The formula for finding the perimeter is Side A +
Side B + Side A + Side B. This could also be stated as 2*Side A +
2*Side B or 2*(Side A + Side B).

Calculating the Circumference of a Circle
The circumference of a circle is the distance around the outside of the circle. It
could be called the perimeter of the circle.
How to find the circumference of a circle:
The circumference of a circle can be found by multiplying pi ( π
= 3.14 ) by the diameter of the circle.
If a circle has a diameter of 4, its circumference is
3.14*4=12.56
If you know the radius, the diameter is twice as large.

Calculate the Surface Area of a Cube
To calculate the surface are of a cube, find the surface area of one
side and multiply by 6. The surface area of any side is the length of a
side squared.

Example: Surface area of a cube with a side of length 4 = 4*4*6 = 96


Surface Area of Rectangular Prisms
A rectangular prism has 2 ends and 4 sides. Opposite sides have the same area.
The surface area is the sum of the areas of all six sides.
How to find the surface area of Rectangular Prisms:
Find the area of two sides (Length*Height)*2 sides
Find the area of adjacent sides (Width*Height)*2 sides
Find the area of ends (Length*Width)*2 ends
Add the three areas together to find the surface area

5. Example: The surface area of a rectangular prism 5 cm lon g, 3
cm. wide and 2 cm. high = 5*2*2 + 3*2*2 + 5*3*2 = 20 + 12
+ 30 = 62 cm
2
.

Surface Area of Cylinders.
To find the surface area of a cylinder add the surface area of each end
plus the surface area of the side. Each end is a circle so the surface
area of each end is * r
2
, where r is the radius of the end. There are
two ends so their combinded surface area is 2 * r
2
. The surface area
of the side is the circumference times the height or 2 * r * h, where
r is the radius and h is the height of the side.
The entire formula for the surface area of a cylinder is 2 r
2
+ 2 r h


Volume of a Cube
The volume of a cube is (length of side)
3
.
Volume of a Rectangular Prism
The volume of a rectangular prism can be found by the formula:
volume=length*width*height

Volume of a Triangular Prism
The volume of a triangular prism can be found by the formula:

volume=1/2*length*width*height.
Volume of a Cone
The volume of a cone is 1/3(Area of Base)(height) = 1/3 π r
2
h

Volume of a Cylinder
The volume of a cylinder equals the (area of the base)*height = π r
2
h

6. Volume of a Pyramid
A pyramid has a base and triangular sides which rise to meet at the same point.
The base may be any polygon such as a square, rectangle, triangle, etc. The
general formula for the volume of a pyramid is:
Area of the base * Height * 1/3
The volume of a pyramid with a rectangular base is equal to:
Length_of_base * Width_of_base * Height * 1/3


Volume of a Sphere
The volume of a sphere can be found by the formula:

volume = 4/3 π r
3