Perimeter and Area of Polygons

1
Perimeter and Area of Polygons
  3108.4.28  Derive and use the formulas for the
area and perimeter of a regular polygon. 
3108.4.27  Use right triangle trigonometry to
find the area and perimeter of quadrilaterals
Jim Smith JCHS
3108.1.9    Expand analysis of units of measure
to include area and volume.
2
PERIMETER
There are many formulas (or shortcuts) for
finding the perimeter of polygons. The only one
you need to remember is.
ADD ALL SIDES
This will work for all polygons
3
8
5
5
3
3
4
4
8
8
7
P 383822
P 4554725
P 99422
13
9
9
7
7
P 1374731
4
4
4
Area of Rectangles
Think of filling the rectangle with boxes. All
answers should be in square units.
4
4 Columns By 3 Rows 4X3 12
3
This is the length times the width
A lw
5
Rectangles
38
51
5
12
Alw A51x5 A255 sq units
Alw A38x12 A456 sq units
6
Area of Parallelograms
h
Abh
b
The height must form a right angle with a base
7
Parallelograms
7
15
6
10
Abh A10x7 A70 sq. units
Abh A15x6 A90 sq. units
8
Area of Triangles
h
h
b
b
A1/2 bh
9
Triangles
7
21
A 147 2 A 73½ A 73.5 sq units
A ½ bh A ½ 7x21 A ½ 147
10
Equilateral or Isosceles Triangle
Right Triangle
60
10
10
8
5v3
60
60
6
10
5
5
A ½ bh A ½ 6 x 8 A 24 Sq. Unit
A ½ bh A ½ 10 x 5v3 A 25v3 Sq. Unit
11
Area of Trapezoids
b1
h
b2
A ½ h( b1 b2 )
12
8
Trapezoid
6
12
A ½ h(b1 b2) A ½ (6)( 812 ) A 3( 20 ) A
60 sq units
13
Trapezoid with 45
8
6
45
6
8
14
A ½ h(b1 b2) A ½ 6( 814 ) A ½ 6(22) A
66 sq units
14
Isosceles Trapezoid
6
5v3
6
60
5
5
16
5
A1/2 h( b1b2 ) A ½ 5v3 ( 616 ) A ½ 5v3 ( 22
) A 5v3 ( 11 ) A 55v3 sq units
15
Area of Rhombi and Kites
d1
d2
d1
d2
( d1 and d2 are the whole diagonals )
A ½ d1 x d2
16
Rhombus and Kite
10
8
4
6
7
X
3
6
8
4
A ½ d1 x d2 A ½ 12x16 A 96 sq units
A ½ d1 x d2 A ½ 8x10 A 40 sq units
17
Area of Regular Polygons
s side a apothem r radius
r
a
s
A1/2 aP
18
Regular Hexagon
P 6x6 P 36
5
4
3²x² 5²
6
3
3
A ½ aP A ½ 4x36 A 72 sq units
19
The area of any figure is the sum of all the
non-overlapping parts
Triangle
Trapezoid
Rectangle
20

Add The Parts
OR
21
Complete the figure and subtract the part you
dont want
( bake the
cake and eat the part you dont want! )