Polygons and Area

A polygon is a figure with straight, connected sides.

Polygons:
 

Number of sides Polygon
3 triangle
4 quadrilateral
5 pentagon
6 hexagon
7 heptagon
8 octagon
9 nonagon
10 decagon
12 dodecagon
n n-gon

 

A regular polygon is a polygon with congruent sides and congruent angles.

Interior angle sum = 180(n-2)   {n is number of sides}

Exterior angle sum = 360

The sum of the interior and exterior angles measure 180 degrees.
EX: Find the exterior angle if the interior angle is 45.
180 - 45 = 135

To find the number of sides, divide 360 by exterior angle.
(because exterior angle sum is always 360)
EX: Find the number of sides given the exterior angle is 45.
360/45 = 8 sides
EX 2: Find the exterior angle given there are 9 sides.
360/9 = 40 degrees

If you are given one interior angle, subtract from 180 to get exterior angle, then divide 360 by exterior angle.
EX: Find the number of sides given the interior angle is 108.
180 - 108 = 72 then 360/72 = 5 sides

 

Only need Area Formulas from this formula sheet for this chapter:

                 Examples:                       

1. Find the area of the triangle              

                      

Find the base first:   
x2 + 92 = 152  then x = 12
  Then A = 1/2bh for a triangle thus      (1/2)(12)(9).
    *Never use the hypotenuse for  the  area of a triangle.

2. Find the perimeter and area of the trapezoid               
 

P = 10+8+8+16 = 42 in
           A=(1/2)h(b+b)
(1/2)(12)(10+16)
A =156in2  

 

3. Find the area and perimeter of the equilateral triangle base
    with sides 6in.
    Have to use Pythagorean theorem to find the height of the triangle:
      

h2 + 32 = 62
h = 5.2 m
Area of the triangular base is (1/2)(5.2)(6)
Area = 15.6 m2
Perimeter of the triangular base is 6+6+6
Perimeter = 18 m

                                                  

Example Problems


3. Find the sum of the measure of the interior angles of a
    pentagon.
4. How many sides does a polygon have if the exterior angle
    measures 20?
5. Find the area of a rhombus with diagonals 15 in and 17 in.
6. Find the area of a circle with diameter of 16 ft.
7. Find the circumference of a circle with radius of 22 m.
8. Find the number of sides of a polygon if the interior angle
    measures 165.
9. Find the area of a triangle with base 8 in and height 12 in.
10. Find the area of an equilateral triangle with sides 10 in.